We theoretically analyze the intensity of the resonant inelastic X-ray scattering (RIXS) based on Ansatz that the electron is fractionalized into two components. By fitting the angle resolved photoemission spectroscopy (ARPES) data of a cuprate high-T-c superconductor Bi2Sr2CaCu2O8+delta and the subsequent machine learning results obtained before by Yamaji et al. (arXiv:1903.08060), we determine the parameters of the two-component fermion model that describes the electron fractionalization. The RIXS spectra are predicted based on this formulation. We find that the intensity is enhanced in the superconducting phase relative to the normal or pseudogap phase. Since the enhancement is unusual, we propose this can be used as a critical test whether the unconventional electron fractionalization captures the essence of the cuprate superconductivity. This type of combined analyses using multiple independent spectroscopy data, with the help of theoretical and machine learning insights, regarded as integrated spectroscopy opens a new route to study difficult open issues in strongly correlated electron systems.

Despite decades of intense theoretical, experimental and computational effort, a microscopic theory of high-temperature superconductivity is not yet established. Eight researchers share their contributions to the search for a better understanding of unconventional superconductivity and their hopes for the future of the field.

Using a cluster extension of the dynamical mean-field theory (CDMFT) we map out the magnetic phase diagram of the anisotropic square lattice Hubbard model with nearest-neighbor intrachain t and interchain t(perpendicular to) hopping amplitudes at half filling. A fixed value of the next-nearest-neighbor hopping t' = -t(perpendicular to)/2 removes the nesting property of the Fermi surface and stabilizes a paramagnetic metal phase in the weak-coupling regime. In the isotropic and moderately anisotropic regions, a growing spin entropy in the metal phase is quenched out at a critical interaction strength by the onset of long-range antiferromagnetic (AF) order of preformed local moments. It gives rise to a first-order metal-insulator transition consistent with the Mott-Heisenberg picture. In contrast, a strongly anisotropic regime t(perpendicular to)/t less than or similar to 0.3 displays a quantum critical behavior related to the continuous transition between an AF metal phase and the AF insulator. Hence, within the present framework of CDMFT, the opening of the charge gap is magnetically driven as advocated in the Slater picture. We also discuss how the lattice-anisotropy-induced evolution of the electronic structure on a metallic side of the phase diagram is tied to the emergence of quantum criticality.

A method to calculate the one-body Green's function for ground states of correlated electron materials is formulated by extending the variational Monte Carlo method. We benchmark against the exact diagonalization (ED) for the one- and two-dimensional Hubbard models of 16-site lattices, which proves high accuracy of the method. The application of the method to a larger-sized Hubbard model on the square lattice correctly reproduces the Mott insulating behavior at half-filling and gap structures of the d-wave superconducting state of the hole-doped Hubbard model in the ground state optimized by enforcing the charge uniformity, evidencing a wide applicability to strongly correlated electron systems. From the obtained d-wave superconducting gap of the charge-uniform state, we find that the gap amplitude at the antinodal point is several times larger than the experimental value when we employ a realistic parameter as a model of the cuprate superconductors. The effective attractive interaction of carriers in the d-wave superconducting state inferred for an optimized state of the Hubbard model is as large as the order of the nearest-neighbor transfer, which is far beyond the former expectation in the cuprates. We discuss the nature of the superconducting state of the Hubbard model in terms of the overestimate of the gap and the attractive interaction in comparison to the cuprates.

We propose a method to calculate the charge dynamical structure factors for the ground states of correlated electron systems based on the variational Monte Carlo method. Our benchmarks for the one- and two-dimensional Hubbard models show that inclusion of composite-fermion excitations in the basis set greatly improves the accuracy, in reference to the exact charge dynamical structure factors for clusters. Together with examination for larger systems beyond tractable sizes by the exact diagonalization, our results indicate that the variational Monte Carlo method is a promising way for studies on the nature of charge dynamics in correlated materials such as the copper oxide superconductors if the composite-fermion excitations are properly included in the restricted Hilbert space of intermediate states in the linear response theory. Our results are consistent with the particle-hole excitations inferred from the single-particle spectral function A(k, omega) in the literature. We also discuss the importance of incorporating nonlocal composite fermion for a more accurate description. Future issues for further improvements are also discussed.

Understanding physics of high-Tc cuprate superconductors remains one of the important problems in materials science. Though a number of diverse theories argue about the superconductivity and competing orders, ab initio and quantitative understanding is lacking. Here, we reproduce the experimental phase diagram of HgBa2CuO4+y by solving its ab initio low-energy effective Hamiltonian without adjustable parameters. It shows a superconducting phase in a wide range of hole density δ, and its competition with charge period-4 plus spin period-8 stripe order near δ∼0.1, in agreement with experimental results including recent x-ray scattering. Then a crucial role of off-site interactions in stabilizing the superconductivity is elucidated with emphasis on charge fluctuations. It also clarifies the condensation energy mainly contributed from the on-site Coulomb interaction. The present achievement will enable deeper, predictable understanding on open issues of the high-Tc superconducting mechanism and promote ab initio studies on strongly correlated electrons beyond parametrized model studies.

Three types (three-band, two-band, and one-band) of effective Hamiltonians for HgBa2CuO4 and three-band effective Hamiltonian for La2CuO4 are derived by improving the constrained-GW approximation combined with the self-interaction correction (cGW-SIC) formulated by Hirayama et al. [Phys. Rev. B 98, 134501 (2018)2469-995010.1103/PhysRevB.98.134501]. The improved treatment of the interband Hartree energy in the present paper turns out to be crucially important, because the solution of the present improved Hamiltonian shows excellent agreement with the experimental results, for instance, for the charge gap (2 eV) and antiferromagnetic ordered moment (0.6μB) of the mother compound of La2CuO4, in sharp contrast to the estimates by the previous Hamiltonian, 4.5 eV and 0.8μB, respectively. To our knowledge, this is the first simultaneous and quantitative reproduction of these quantities by abinitio methods without introducing adjustable parameters. We also predict that the Mott gap and the magnetic ordered moment for HgBa2CuO4 is about 0.7 eV and 0.4μB, respectively, if the mother compound becomes available, indicating weaker electron correlations than La2CuO4. Surprisingly, we find that while carriers are doped only in the highest antibonding band, only the Cu 3dx2-y2 (O 2p) carriers look doped in the electron (hole) doped side around the zero doping in the atomic orbital basis, implying that the Mott-Hubbard (single-band) and charge transfer (three-band) descriptions are both correct. The obtained Hamiltonians will serve to further clarify the electronic structures of these copper oxide superconductors and to elucidate the superconducting mechanism in an ab initio fashion.

We formulate a method of deriving an effective low-energy Hamiltonian for nonperiodic systems such as interfaces for strongly correlated electron systems by extending a conventional multiscale ab initio scheme for correlated electrons (MACE). We apply the formalism to copper-oxide high Tc superconductors in an example of the interface between overdoped La2-xSrxCuO4 and Mott insulating La2CuO4 recently realized experimentally and derive the two-band effective Hamiltonian (Eg Hamiltonian) from the Cu 3dx2-y2-like and 3d3r2-z2-like orbitals near the Fermi level. We show that the parameters of the Eg Hamiltonian derived for the La2CuO4/La1.55Sr0.45CuO4 superlattice differ considerably from those for the bulk La2CuO4, particularly significant in the partially screened Coulomb parameters and the level offset between the dx2-y2 and dz2 orbitals, ΔE. In addition, we investigate the effect of the lattice relaxation on the Eg Hamiltonian by carefully comparing the parameters derived before and after the structure optimization. We find that the CuO6 octahedra distort after the relaxation as a consequence of the Madelung potential difference between the La2CuO4 and La1.55Sr0.45CuO4 sides, by which the layer dependence of the hopping and Coulomb parameters becomes more gradual than the unrelaxed case. Furthermore, the structure relaxation dramatically changes the ΔE value and the occupation number at the interface. This study not only evidences the importance of the ionic relaxation around interfaces but also provides a set of layer-dependent parameters of the Eg Hamiltonian, which is expected to provide further insight into the interfacial superconductivity when solved with low-energy solvers.

mVMC (many-variable Variational Monte Carlo) is an open-source software package based on the variational Monte Carlo method applicable for a wide range of Hamiltonians for interacting fermion systems. In mVMC, we introduce more than ten thousands variational parameters and simultaneously optimize them by using the stochastic reconfiguration (SR) method. In this paper, we explain basics and user interfaces of mVMC. By using mVMC, users can perform the calculation by preparing only one input file of about ten lines for widely studied quantum lattice models, and can also perform it for general Hamiltonians by preparing several additional input files. We show the benchmark results of mVMC for the Hubbard model, the Heisenberg model, and the Kondo-lattice model. These benchmark results demonstrate that mVMC provides ground-state and low-energy-excited-state wave functions for interacting fermion systems with high accuracy. Program summary: Program title: mVMC Program Files doi: http://dx.doi.org/10.17632/xhgyp6ncvt.1 Licensing provisions: GNU General Public License version 3 Programming language: C External routines/libraries: MPI, BLAS, LAPACK, Pfapack, ScaLAPACK (optional) Nature of problem: Physical properties (such as the charge/spin structure factors) of strongly correlated electrons at zero temperature. Solution method: Application software based on the variational Monte Carlo method for quantum lattice model such as the Hubbard model, the Heisenberg model and the Kondo model. Unusual features: It is possible to perform the highly-accurate calculations for ground states in a wide range of theoretical Hamiltonians in quantum many-body systems. In addition to the conventional orders such as magnetic and/or charge orders, user can treat the anisotropic superconductivities within the same framework. This flexibility is the main advantage of mVMC.

Theory of doped Mott insulators is revisited in the light of recent understanding on the singular self-energy structure of the single-particle Green’s function. The unique pole structure in the self-energy induces the high-temperature superconductivity in the anomalous part, while it generates Mott gap and pseudogap in the normal part. Here, we elucidate that fractionalization of electrons, which is exactly hold in the Mott insulator in the atomic limit, more generally produces the emergent Mott-gap fermion and dark (hidden) fermions. It does not require any spontaneous symmetry breaking. The two gaps are the consequences of the hybridization of these two fermions with quasiparticles. We further propose that the Mott-gap fermion and dark fermions are the fermionic component of Frenkel- and Wannier-type excitons, respectively, which coexist in the doped Mott insulator. The Bose–Einstein condensation of the Frenkel-type excitons allowed without spontaneous symmetry breaking holds a key for understanding the unique pole structure and the pseudogap through the instantaneous hybridization between the fractionalized quasiparticle and the dark fermion in analogy with the Mott gap. We argue that the high-T superconductivity is ascribed to the dipole attraction of the Wannier-type excitons. The gap formation mechanism is compared with that caused by conventional spontaneous symmetry breaking known over condensed matter and elementary particle physics including quantum chromodynamics. We propose a numerical framework to test this idea and concept, and discuss experimental ways to find evidences. c

Obtaining accurate properties of many-body interacting quantum matter is a long-standing challenge in theoretical physics and chemistry, rooting into the complexity of the many-body wave-function. Classical representations of many-body states constitute a key tool for both analytical and numerical approaches to interacting quantum problems. Here, we introduce a technique to construct classical representations of many-body quantum systems based on artificial neural networks. Our constructions are based on the deep Boltzmann machine architecture, in which two layers of hidden neurons mediate quantum correlations. The approach reproduces the exact imaginary-time evolution for many-body lattice Hamiltonians, is completely deterministic, and yields networks with a polynomially-scaling number of neurons. We provide examples where physical properties of spin Hamiltonians can be efficiently obtained. Also, we show how systematic improvements upon existing restricted Boltzmann machines ansatze can be obtained. Our method is an alternative to the standard path integral and opens new routes in representing quantum many-body states.

Understanding rare events in turbulence provides a basis for the science of extreme weather, for which the atmosphere is modeled by Navier-Stokes equations (NSEs). In solutions of NSEs for isotropic fluids, various quantities, such as fluid velocities, roughly follow Gaussian distributions, where extreme events are prominent only in small-scale quantities associated with the dissipation-dominating length scale or anomalous scaling regime. Using numerical simulations, this study reveals another universal promotion mechanism at much larger scales if three-dimensional fluids accompany strong two-dimensional anisotropies, as is the case in the atmosphere. The dimensional crossover between two and three dimensions generates prominent fat-tailed non-Gaussian distributions with intermittency accompanied by colossal chainlike structures with densely populated self-organized vortices (serpentinely organized vortices). The promotion is caused by a sudden increase of the available phase space at the crossover length scale. Since the discovered intermittency can involve much larger energies than those in the conventional intermittency in small spatial scales, it governs extreme events and chaotic unpredictability in the synoptic weather system.

The high-temperature superconductivity in copper oxides emerges when carriers are doped into the parent Mott insulator. This well-established fact has, however, eluded a microscopic explanation. Here we show that the missing link is the self-energy pole in the energy-momentum space. Its continuous evolution with doping directly connects the Mott insulator and high-temperature superconductivity. We show this by numerically studying the extremely small doping region close to the Mott insulating phase in a standard model for cuprates, the two-dimensional Hubbard model. We first identify two relevant self-energy structures in the Mott insulator: the pole generating the Mott gap and a relatively broad peak generating the so-called waterfall structure, which is another consequence of strong correlations present in the Mott insulator. We next reveal that either the Mott-gap pole or the waterfall structure (the feature at the energy closer to the Fermi level) directly transforms itself into another self-energy pole at the same energy and momentum when the system is doped with carriers. The anomalous self-energy yielding the superconductivity is simultaneously born exactly at this energy-momentum point. Thus created self-energy pole, interpreted as arising from a hidden fermionic excitation, continuously evolves upon further doping and considerably enhances the superconductivity. Above the critical temperature, the same self-energy pole generates a pseudogap in the normal state. We thus elucidate a unified Mott-physics mechanism, where the self-energy structure inherent to the Mott insulator directly gives birth to both the high critical superconducting temperature and pseudogap.

The long-studied Hubbard model is one of the simplest models of copper-oxide superconductors. However, the connection between the model and the experimental phase diagram is still under debate, in particular regarding the existence and extent of the d-wave superconducting phase. Recent rapid progress in improving the accuracy of numerical solvers has opened a way to answer this question reliably. Here, we study the hole-doping concentration (δ) dependence of the Hubbard model in the ground states on a square lattice at strong coupling U/t=10, for the on-site interaction U and the transfer t, using a variational Monte Carlo method. The method, which combines tensor network and Lanczos methods on top of Pfaffian wave functions, reveals a rich phase diagram, in which many orders compete severely and degenerate within the energy range of 0.01t. We have identified distinct phases including a uniform d-wave superconducting phase for 0.17δ0.22 and a stripe charge/spin ordered phase for δ0.17 with the stripe period depending on δ, together with presumable spatially coexisting antiferromagnetic and stripe order for δ0.07 and coexisting stripe and d-wave superconductivity for 0.07δ0.17. The present, improved method revealed a wider region of a charge uniform superconducting phase than the previous studies and shows a qualitative similarity to the phase diagram of the cuprate superconductors. The superconducting order parameter is largest at doping of around δ=0.17 in the ground state, which undergoes phase transitions from an inhomogeneous to a uniform state.

Ab initio low-energy effective Hamiltonians of two typical high-temperature copper-oxide superconductors, whose mother compounds are La2CuO4 and HgBa2CuO4, are derived by utilizing the multiscale ab initio scheme for correlated electrons (MACE). The effective Hamiltonians obtained in the present study serve as platforms of future studies to accurately solve the low-energy effective Hamiltonians beyond the density functional theory. It allows further study on the superconducting mechanism from first principles and a quantitative basis without adjustable parameters not only for the available cuprates but also for future design of higher Tc in general. More concretely, we derive effective Hamiltonians for three variations: (1) a one-band Hamiltonian for the antibonding orbital generated from strongly hybridized Cu 3dx2-y2 and O 2pσ orbitals, (2) a two-band Hamiltonian constructed from the antibonding orbital and Cu 3d3z2-r2 orbital hybridized mainly with the apex oxygen pz orbital, and (3) a three-band Hamiltonian consisting mainly of Cu 3dx2-y2 orbitals and two O 2pσ orbitals. Differences between the Hamiltonians for La2CuO4 and HgBa2CuO4, which have relatively low and high critical temperatures Tc, respectively, at optimally doped compounds, are elucidated. The main differences are summarized as follows: (i) the oxygen 2pσ orbitals are farther (∼3.7 eV) below from the Cu dx2-y2 orbital in the case of the La compound than the Hg compound (∼2.4 eV) in the three-band Hamiltonian. This causes a substantial difference in the character of the dx2-y2-2pσ antibonding band at the Fermi level and makes the effective onsite Coulomb interaction U larger for the La compound than the Hg compound for the two- and one-band Hamiltonians. (ii) The ratio of the second-neighbor to the nearest transfer t′/t is also substantially different (0.26 for the Hg and 0.15 for the La compound) in the one-band Hamiltonian. Heavier entanglement of the two bands in the two-band Hamiltonian implies that the two-band rather than the one-band Hamiltonian is more appropriate for the La compound. The relevance of the three-band description is also discussed especially for the Hg compound.

We study competitions among charge-uniform and -inhomogeneous states in two-dimensional Hubbard models by using a variational Monte Carlo method. At realistic parameters for cuprate superconductors, emergent effective attraction of carriers generated from repulsive Coulomb interaction leads to charge/spin stripe ground states, which severely compete with uniform superconducting excited states in the energy scale of 10 K for cuprates. Stripe period increases with decreasing hole doping δ, which agrees with the experiments for La-based cuprates at δ=1/8. For lower δ, we find a phase separation. Implications of the emergent attraction for cuprates are discussed.

We develop a machine learning method to construct accurate ground-state wave functions of strongly interacting and entangled quantum spin as well as fermionic models on lattices. A restricted Boltzmann machine algorithm in the form of an artificial neural network is combined with a conventional variational Monte Carlo method with pair product (geminal) wave functions and quantum number projections. The combination allows an application of the machine learning scheme to interacting fermionic systems. The combined method substantially improves the accuracy beyond that ever achieved by each method separately, in the Heisenberg as well as Hubbard models on square lattices, thus proving its power as a highly accurate quantum many-body solver.

Using a variational Monte Carlo method, we study the competition of strong electron-electron and electron-phonon interactions in the ground state of the Holstein-Hubbard model on a square lattice. At half filling, an extended intermediate metallic or weakly superconducting (SC) phase emerges, sandwiched between antiferromagnetic and charge order (CO) insulating phases. By carrier doping into the CO insulator, the SC order dramatically increases for strong electron-phonon couplings, but is largely hampered by wide phase separation (PS) regions. Superconductivity is optimized at the border to the PS.

The conventional tensor-network states employ real-space product states as reference wave functions. Here, we propose a many-variable variationalMonte Carlo (mVMC) method combined with tensor networks by taking advantages of both to study fermionic models. The variational wave function is composed of a pair product wave function operated by real-space correlation factors and tensor networks. Moreover, we can apply quantum number projections, such as spin, momentum, and lattice symmetry projections, to recover the symmetry of the wave function to further improve the accuracy. We benchmark our method for one-and two-dimensional Hubbard models, which show significant improvement over the results obtained individually either by mVMC or by tensor network. We have applied the present method to a hole-doped Hubbard model on the square lattice, which indicates the stripe charge/spin order coexisting with a weak d-wave superconducting order in the ground state for the doping concentration of less than 0.3, where the stripe oscillation period gets longer with increasing hole concentration. The charge homogeneous and highly superconducting state also exists as a metastable excited state for the doping concentration less than 0.25.

We propose a refined scheme of deriving an effective low-energy Hamiltonian for materials with strong electronic Coulomb correlations beyond density functional theory (DFT). By tracing out the electronic states away from the target degrees of freedom in a controlled way by a perturbative scheme, we construct an effective Hamiltonian for a restricted low-energy target space incorporating the effects of high-energy degrees of freedom in an effective manner. The resulting effective Hamiltonian can afterwards be solved by accurate many-body solvers. We improve this "multiscale ab initio scheme for correlated electrons" (MACE) primarily in two directions by elaborating and combining two frameworks developed by Hirayama et al. [M. Hirayama, T. Miyake, and M. Imada, Phys. Rev. B 87, 195144 (2013)PRBMDO1098-012110.1103/PhysRevB.87.195144] and Casula et al. [M. Casula, P. Werner, L. Vaugier, F. Aryasetiawan, T. Miyake, A. J. Millis, and S. Biermann, Phys. Rev. Lett. 109, 126408 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.126408]: (1) Double counting of electronic correlations between the DFT and the low-energy solver is avoided by using the constrained GW scheme; and (2) the frequency dependent interactions emerging from the partial trace summation are successfully separated into a nonlocal part that is treated following ideas by Hirayama et al. and a local part treated nonperturbatively in the spirit of Casula et al. and are incorporated into the renormalization of the low-energy dispersion. The scheme is favorably tested on the example of SrVO3.

We investigate the ground state properties of Na IrO based on numerical calculations of the recently proposed ab initio Hamiltonian represented by Kitaev and extended Heisenberg interactions. To overcome the limitation posed by small tractable system sizes in the exact diagonalization study employed in a previous study [Y.Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014)], we apply a two-dimensional density matrix renormalization group and an infinite-size tensor-network method. By calculating at much larger system sizes, we critically test the validity of the exact diagonalization results. The results consistently indicate that the ground state of Na IrO is a magnetically ordered state with zigzag configuration in agreement with experimental observations and the previous diagonalization study. Applications of the two independent methods in addition to the exact diagonalization study further uncover a consistent and rich phase diagram near the zigzag phase beyond the accessibility of the exact diagonalization. For example, in the parameter space away from the ab initio value of Na IrO controlled by the trigonal distortion, we find three phases: (i) an ordered phase with the magnetic moment aligned mutually in 120 degrees orientation on every third hexagon, (ii) a magnetically ordered phase with a 16-site unit cell, and (iii) an ordered phase with presumably incommensurate periodicity of the moment. It suggests that potentially rich magnetic structures may appear in A IrO compounds for A other than Na. The present results also serve to establish the accuracy of the first-principles approach in reproducing the available experimental results thereby further contributing to finding a route to realize the Kitaev spin liquid. 2 3 2 3 2 3 2 3

Studies on out-of-equilibrium dynamics have paved a way to realize a new state of matter. Superconductor-like properties above room temperatures recently suggested to be in copper oxides achieved by selectively exciting vibrational phonon modes by laser have inspired studies on an alternative and general strategy to be pursued for high-temperature superconductivity. We show that the superconductivity can be enhanced by irradiating laser to correlated electron systems owing to two mechanisms: First, the effective attractive interaction of carriers is enhanced by the dynamical localization mechanism, which drives the system into strong coupling regions. Second, the irradiation allows reaching uniform and enhanced superconductivity dynamically stabilized without deteriorating into equilibrium inhomogeneities that suppress superconductivity. The dynamical superconductivity is subject to the Higgs oscillations during and after the irradiation. Our finding sheds light on a way to enhance superconductivity that is inaccessible in equilibrium in strongly correlated electron systems.

Realization and design of topological insulators emerging from electron correlations, called topological Mott insulators (TMIs), is pursued by using mean-field approximations as well as multi-variable variational Monte Carlo (MVMC) methods for Dirac electrons on honeycomb lattices. The topological insulator phases predicted in the previous studies by the mean-field approximation for an extended Hubbard model on the honeycomb lattice turn out to disappear, when we consider the possibility of a long-period charge-density-wave (CDW) order taking over the TMI phase. Nevertheless, we further show that the TMI phase is still stabilized when we are able to tune the Fermi velocity of the Dirac point of the electron band. Beyond the limitation of the mean-field calculation, we apply the newly developed MVMC to make accurate predictions after including the many-body and quantum fluctuations. By taking the extrapolation to the thermodynamic and weak external field limit, we present realistic criteria for the emergence of the topological insulator caused by the electron correlations. By suppressing the Fermi velocity to a tenth of that of the original honeycomb lattice, the topological insulator emerges in an extended region as a spontaneous symmetry breaking surviving competitions with other orders. We discuss experimental ways to realize it in a bilayer graphene system.

Relaxation of electrons in a Hubbard ring coupled to a dissipative bosonic bath is studied to simulate the pump-probe photoemission measurement. From this insight, we propose an experimental method of eliciting the unoccupied part of single-particle spectra at the equilibrium of doped Mott insulators. We reveal first that the effective temperatures of distribution functions and electronic spectra are different during the relaxation, which makes the frequently employed thermalization picture inappropriate. Contrary to the conventional analysis, we show that the unoccupied spectra at equilibrium can be detected as the states that relax faster.

We study the frequency-dependent structure of electronic self-energy in the pseudogap and superconducting states of the two-dimensional Hubbard model. We present the self-energy calculated with the cellular dynamical mean-field theory systematically in the space of temperature, electron density, and interaction strength. We show that the low-frequency part of the self-energy is well represented by a simple equation, which describes the transitions of an electron to and from a hidden-fermionic state. By fitting the numerical data with this simple equation, we determine the parameters characterizing the hidden fermion and discuss its identity. The simple expression of the self-energy offers a way to organize numerical data of these uncomprehended superconducting and pseudogap states, as well as a useful tool to analyze spectroscopic experimental results. The successful description by the simple two-component fermion model supports the idea of "dark" and "bright" fermions emerging from a bare electron as bistable excitations in doped Mott insulators.

RENiO3 (RE = rare-earth element) and V2O3 are archetypal Mott insulator systems. When tuned by chemical substitution (RENiO3) or pressure (V2O3), they exhibit a quantum phase transition (QPT) between an antiferromagnetic Mott insulating state and a paramagnetic metallic state. Because novel physics often appears near a Mott QPT, the details of this transition, such as whether it is first or second order, are important. Here, we demonstrate through muon spin relaxation/rotation (mSR) experiments that the QPT in RENiO3 and V2O3 is first order: the magnetically ordered volume fraction decreases to zero at the QPT, resulting in a broad region of intrinsic phase separation, while the ordered magnetic moment retains its full value until it is suddenly destroyed at the QPT. These findings bring to light a surprising universality of the pressure-driven Mott transition, revealing the importance of phase separation and calling for further investigation into the nature of quantum fluctuations underlying the transition.

Stabilizing superconductivity at high temperatures and elucidating its mechanism have long been major challenges of materials research in condensed matter physics. Meanwhile, recent progress in nanostructuring offers unprecedented possibilities for designing novel functionalities. Above all, thin films of cuprate and iron-based high-temperature superconductors exhibit remarkably better superconducting characteristics (for example, higher critical temperatures) than in the bulk, but the underlying mechanism is still not understood. Solving microscopic models suitable for cuprates, we demonstrate that, at an interface between a Mott insulator and an overdoped nonsuperconducting metal, the superconducting amplitude is always pinned at the optimum achieved in the bulk, independently of the carrier concentration in the metal. This is in contrast to the dome-like dependence in bulk superconductors but consistent with the astonishing independence of the critical temperature from the carrier density x observed at the interfaces of La2CuO4 and La2-xSrxCuO4. Furthermore, we identify a self-organization mechanism as responsible for the pinning at the optimum amplitude: An emergent electronic structure induced by interlayer phase separation eludes bulk phase separation and inhomogeneities that would kill superconductivity in the bulk. Thus, interfaces provide an ideal tool to enhance and stabilize superconductivity. This interfacial example opens up further ways of shaping superconductivity by suppressing competing instabilities, with direct perspectives for designing devices.

We propose real-space renormalized dynamical mean field theory (rr-DMFT) to deal with large clusters in the framework of a cluster extension of the DMFT. In the rr-DMFT, large clusters are decomposed into multiple smaller clusters through a real-space renormalization. In this work, the renormalization effect is taken into account only at the lowest order with respect to the intercluster coupling, which nonetheless reproduces exactly both the noninteracting and atomic limits. Our method allows us large cluster-size calculations which are intractable with the conventional cluster extensions of the DMFT with impurity solvers, such as the continuous-time quantum Monte Carlo and exact diagonalization methods. We benchmark the rr-DMFT for the two-dimensional Hubbard model on a square lattice at and away from half filling, where the spatial correlations play important roles. Our results on the spin structure factor indicate that the growth of the antiferromagnetic spin correlation is taken into account beyond the decomposed cluster size. We also show that the self-energy obtained from the large-cluster solver is reproduced by our method better than the solution obtained directly for the smaller cluster. When applied to the Mott metal-insulator transition, the rr-DMFT is able to reproduce the reduced critical value for the Coulomb interaction comparable to the large cluster result.

Contrary to the original expectation, Na2IrO3 is not a Kitaev's quantum spin liquid (QSL) but shows a zigzag-type antiferromagnetic order in experiments. Here, we propose experimental clues and criteria to measure how a material in hand is close to the Kitaev's QSL state. For this purpose, we systematically study thermal and spin excitations of a generalized Kitaev-Heisenberg model studied by Chaloupka et al., Phys. Rev. Lett. 110, 097204 (2013) and an effective ab initio Hamiltonian for Na2IrO3 proposed by Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014), by employing a numerical diagonalization method. We reveal that closeness to the Kitaev's QSL is characterized by the following properties, besides trivial criteria such as reduction of magnetic ordered moments and Neel temperatures. (1) Two peaks in the temperature dependence of specific heat at T-l and T-h caused by the fractionalization of spin to two types of Majorana fermions. (2) In between the double peak, a prominent plateau or shoulder pinned at R/2 ln 2 in the temperature dependence of entropy, where R is the gas constant. (3) Failure of the linear spin wave approximation at the low-lying excitations of dynamical structure factors. (4) Small ratio T-l/T-h close to or less than 0.03. According to the proposed criteria, Na2IrO3 is categorized to a compound close to the Kitaev's QSL, and is proven to be a promising candidate for the realization of the QSL if the relevant material parameters can further be tuned by making thin film of Na2IrO3 on various substrates or applying axial pressure perpendicular to the honeycomb networks of iridium ions. Applications of these characterization to (Na1-x Li-x)(2)IrO3 and other related materials are also discussed.

Spontaneous symmetry breakings, metal-insulator transitions, and transport properties of magnetic-domain-wall states in pyrochlore iridium oxides are studied by employing a symmetry-adapted effective Hamiltonian with a slab perpendicular to the (111) direction of the pyrochlore structure. Emergent metallic domain wall, which has an unconventional topological nature with a controllable and mobile metallic layer, is shown to host Fermi surfaces with modulated helical spin textures resembling Rashba metals. The helical nature of the domain-wall Fermi surfaces is experimentally detectable by anomalous Hall conductivity, circular dichroism, and optical Hall conductivity under external magnetic fields. Possible applications of the domain-wall metals to spin-current generation and "half-metallic" conduction are also discussed.

A new computational method for finite-temperature properties of strongly correlated electrons is proposed by extending the variational Monte Carlo method originally developed for the ground state. The method is based on the path integral in the imaginary-time formulation, starting from the infinite-temperature state that is well approximated by a small number of certain random initial states. Lower temperatures are progressively reached by the imaginary-time evolution. The algorithm follows the framework of the quantum transfer matrix and finite-temperature Lanczos methods, but we extend them to treat much larger system sizes without the negative sign problem by optimizing the truncated Hilbert space on the basis of the time-dependent variational principle (TDVP). This optimization algorithm is equivalent to the stochastic reconfiguration (SR) method that has been frequently used for the ground state to optimally truncate the Hilbert space. The obtained finite-temperature states allow an interpretation based on the thermal pure quantum (TPQ) state instead of the conventional canonical-ensemble average. Our method is tested for the one-and two-dimensional Hubbard models and its accuracy and efficiency are demonstrated.

We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor renormalization group and the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.

The dynamics of a microscopic cuprate model, namely, the two-dimensional Hubbard model, is studied with a cluster extension of the dynamical mean-field theory. We find a nontrivial structure of the frequency-dependent self-energies, which describes an unprecedented interplay between the pseudogap and superconductivity. We show that these properties are well described by quasiparticles hybridizing with (hidden) fermionic excitations, emergent from the strong electronic correlations. The hidden fermion enhances superconductivity via a mechanism distinct from a conventional boson-mediated pairing, and originates the normal-state pseudogap. Though the hidden fermion is elusive in experiments, it can solve many experimental puzzles.

We develop a time-dependent variational Monte Carlo (t-VMC) method for quantum dynamics of strongly correlated electrons. The t-VMC method has been recently applied to bosonic systems and quantum spin systems. Here we propose a time-dependent trial wave function with many variational parameters, which is suitable for nonequilibrium strongly correlated electron systems. As the trial state, we adopt the generalized pair-product wave function with correlation factors and quantum-number projections. This trial wave function has been proven to accurately describe ground states of strongly correlated electron systems. To show the accuracy and efficiency of our trial wave function in nonequilibrium states as well, we present our benchmark results for relaxation dynamics during and after interaction quench protocols of fermionic Hubbard models. We find that our trial wave function well reproduces the exact results for the time evolution of physical quantities such as energy, momentum distribution, spin structure factor, and superconducting correlations. These results show that the t-VMC with our trial wave function offers an efficient and accurate way to study challenging problems of nonequilibrium dynamics in strongly correlated electron systems.

© 2015 American Physical Society. We develop a time-dependent variational Monte Carlo (t-VMC) method for quantum dynamics of strongly correlated electrons. The t-VMC method has been recently applied to bosonic systems and quantum spin systems. Here we propose a time-dependent trial wave function with many variational parameters, which is suitable for nonequilibrium strongly correlated electron systems. As the trial state, we adopt the generalized pair-product wave function with correlation factors and quantum-number projections. This trial wave function has been proven to accurately describe ground states of strongly correlated electron systems. To show the accuracy and efficiency of our trial wave function in nonequilibrium states as well, we present our benchmark results for relaxation dynamics during and after interaction quench protocols of fermionic Hubbard models. We find that our trial wave function well reproduces the exact results for the time evolution of physical quantities such as energy, momentum distribution, spin structure factor, and superconducting correlations. These results show that the t-VMC with our trial wave function offers an efficient and accurate way to study challenging problems of nonequilibrium dynamics in strongly correlated electron systems.

We study the attractive Hubbard model within the dynamical mean-field theory, to elucidate how the pseudogap and superconductivity at strong attractive interaction are related to those found in the repulsive Hubbard model, and thereby to bridge cold fermions and cuprate high-temperature superconductors from a microscopic point of view. We propose that a unified understanding is obtained by investigating single-particle excitation dynamics, in which emergent and hidden fermions coupled to quasiparticles consistently account for the numerical results in both attractive and repulsive cases. In the attractive case, the quasiparticle dynamics is observable by virtually breaking a tightly bound pair, where we find two qualitatively different regions crossing over each other within the strong-coupling superconductivity phase. Among them, the region close to the critical temperature shares characteristic dynamics with the repulsive interaction case, where the normal and anomalous parts of the self-energy show strong low-energy peaks while they are hidden in the quasiparticle spectral weight. These prominent self-energy peaks are understood by the coupling of the quasiparticle to the hidden fermionic excitation, emergent from a strong-coupling effect. The pseudogap above the critical temperature is also accounted for by the same hidden fermion.

Energy dissipation and decoherence are at first glance harmful to acquiring the long exciton lifetime desired for efficient photovoltaics. In the presence of both optically forbidden (namely, dark) and allowed (bright) excitons, however, they can be instrumental, as suggested in photosynthesis. By simulating the quantum dynamics of exciton relaxations, we show that the optimized decoherence that imposes a quantum-to-classical crossover with the dissipation realizes a dramatically longer lifetime. In an example of a carbon nanotube, the exciton lifetime increases by nearly 2 orders of magnitude when the crossover triggers a stable high population in the dark excitons.

The iron chalcogenides FeTe and FeSe belong to the family of iron-based superconductors. We study the magnetism in these compounds in the normal state using the ab initio downfolding scheme developed for strongly correlated electron systems. In deriving ab initio low-energy effective models, we employ the constrained GW method to eliminate the double counting of electron correlations originating from the exchange correlations already taken into account in the density functional theory. By solving the derived ab initio effective models, we reveal that the elimination of the double counting is important in reproducing the bicollinear antiferromagnetic order in FeTe, as is observed in experiments. We also show that the elimination of the double counting induces a unique degeneracy of several magnetic orders in FeSe, which may explain the absence of the magnetic ordering. We discuss the relationship between the degeneracy and the recently found puzzling phenomena in FeSe as well as the magnetic ordering found under pressure.

We propose an accurate variational Monte Carlo method applicable in the presence of the strong spin-orbit interactions. The algorithm is applicable even in a wider class of Hamiltonians that do not have the spin-rotational symmetry. Our variational wave functions consist of generalized Pfaffian-Slater wave functions that involve mixtures of singlet and triplet Cooper pairs, Jastrow-Gutzwiller-type projections, and quantum number projections. The generalized wave functions allow describing states including a wide class of symmetry-broken states, ranging from magnetic and/or charge ordered states to superconducting states and their fluctuations, on equal footing without any ad hoc ansatz for variational wave functions. We detail our optimization scheme for the generalized Pfaffian-Slater wave functions with complex-number variational parameters. Generalized quantum number projections are also introduced, which imposes the conservation of not only the momentum quantum number but also Wilson loops. As a demonstration of the capability of the present variational Monte Carlo method, the accuracy and efficiency is tested for the Kitaev and Kitaev-Heisenberg models, which lack the SU( 2) spin-rotational symmetry except at the Heisenberg limit. The Kitaev model serves as a critical benchmark of the present method: The exact ground state of the model is a typical gapless quantum spin liquid far beyond the reach of simple mean-field wave functions. The newly introduced quantum number projections precisely reproduce the ground state degeneracy of the Kitaev spin liquids, in addition to their ground state energy. An application to a closely related itinerant model described by a multiorbital Hubbard model with the spin-orbit interaction also shows promising benchmark results. The strong-coupling limit of the multiorbital Hubbard model is indeed described by the Kitaev model. Our framework offers accurate solutions for the systems where strong electron correlation and spin-orbit interaction coexist.

The nature of quantum spin liquids is studied for the spin-1/2 antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites, J(1), and those between next-nearest-neighbor sites, J(2). We perform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra. We obtain the nonmagnetic phase in the region 0.4 < J(2)/J(1) <= 0.6 sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of 0.4 < J(2)/J(1) <= 0.5, while the gapped valence-bond-crystal (VBC) phase is stabilized for 0.5 < J(2)/J(1) <= 0.6. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the C-4v symmetry. The power-law behaviors of the spin-spin and dimer-dimer correlation functions in the gapless region are consistent with the emergence of the algebraic quantum-spin-liquid phase (critical phase). The exponent of the spin correlation [S(0)S(r)] proportional to 1/r(z+n) at a long distance r appears to increase from z + eta similar to 1 at J(2)/J(1) similar to 0.4 toward the continuous transition to the VBC phase at J(1)/J(1) similar to 0.5. Our results, however, do not fully exclude the possibility of a direct quantum transition between the staggered AF and VBC phases with a wide critical region and deconfined criticality.

Two families of high-temperature superconductors whose critical temperatures are higher than 50 K are known. One are the copper oxides and the other are the iron-based superconductors. Comparisons of mechanisms between these two in terms of common ground as well as distinctions will greatly help in searching for higher T-c superconductors. However, studies on mechanisms for the iron family based on first principles calculations are few. Here we first show that superconductivity emerges in the state-of-the-art numerical calculations for an ab initio multi-orbital model of an electron-doped iron-based superconductor LaFeAsO, in accordance with experimental observations. Then the mechanism of the superconductivity is identified as enhanced uniform density fluctuations by one-to-one correspondence with the instability towards inhomogeneity driven by first-order antiferromagnetic and nematic transitions. Despite many differences, certain common features with the copper oxides are also discovered in terms of the underlying orbital-selective Mottness found in the iron family.

We numerically study the Heisenberg models on triangular lattices by extending it from the simplest equilateral lattice with only the nearest-neighbor exchange interaction. We show that, by including an additional weak next-nearest-neighbor interaction, a quantum spin-liquid phase is stabilized against the antiferromagnetic order. The spin gap (triplet excitation gap) and spin correlation at long distances decay algebraically with increasing system size at the critical point between the antiferromagnetic phase and the spin-liquid phase. This algebraic behavior continues in the spin-liquid phase as well, indicating the presence of an unconventional critical (algebraic spin-liquid) phase characterized by the dynamical and anomalous critical exponents z + eta similar to 1. Unusually small triplet and singlet excitation energies found in extended points of the Brillouin zone impose constraints on this algebraic spin liquid.

An effective low-energy Hamiltonian of itinerant electrons for iridium oxide Na2IrO3 is derived by an ab initio downfolding scheme. The model is then reduced to an effective spin model on a honeycomb lattice by the strong coupling expansion. Here we show that the ab initio model contains spin-spin anisotropic exchange terms in addition to the extensively studied Kitaev and Heisenberg exchange interactions, and allows us to describe the experimentally observed zigzag magnetic order, interpreted as the state stabilized by the antiferromagnetic coupling of the ferromagnetic chains. We clarify possible routes to realize quantum spin liquids from existing Na2IrO3.

The doped Hubbard model is a simple model for high-T-c cuprate superconductors, while its ground state remains a challenge. Here, by performing state-of-the-art variational Monte Carlo calculations for the strong-coupling Hubbard model, we find evidence that the d-wave superconducting phase emerges always near the phase separation region and the superconducting order has one-to-one correspondence with the enhancement of charge compressibility. The order as well as the phase separation are vulnerable to realistic intersite Coulomb interaction, while the superexchange interaction enhances both. An appropriate combination of these two widens the stable superconducting phase.

Topological insulators are found in materials that have elements with strong spin-orbit interaction. However, electron Coulomb repulsion also potentially generates the topological insulators as well as Chern insulators by the mechanism of spontaneous symmetry breaking, which is called topological Mott insulators. The quantum criticality of the transition to the topological Mott insulators from zero-gap semiconductors follows unconventional universality distinct from the Landau-Ginzburg-Wilson scenario. On the pyrochlore lattice, the interplay of the electron correlation and the spin-orbit interaction provides us in a rich phase diagram not only with simple topological insulators but also with Weyl semimetal and topologically distinct antiferromagnetic phases. Magnetic domain wall of the all-in-all-out type antiferromagnetic order offers a promising candidate of magnetically controlled transport, because, even when the Weyl points disappears, the domain wall maintains robust gapless excitations with Fermi surfaces around it embedded in the bulk insulator and bears uniform magnetization simultaneously. The ingap state is protected by a mechanism similar to the solitons in polyacetylene. Puzzling experimental results of pyrochlore iridates are favorably compared with the prediction of the domain wall theory.

Topological insulators, in contrast to ordinary semiconductors, accompany protected metallic surfaces described by Dirac-type fermions. Here, we theoretically show that another emergent two-dimensional metal embedded in the bulk insulator is realized at a magnetic domain wall. The domain wall has long been studied as an ingredient of both old-fashioned and leading-edge spintronics. The domain wall here, as an interface of seemingly trivial antiferromagnetic insulators, emergently realizes a functional interface preserved by zero modes with robust two-dimensional Fermi surfaces, where pyrochlore iridium oxides proposed to host the condensed-matter realization of Weyl fermions offer such examples at low temperatures. The existence of in-gap states that are pinned at domain walls, theoretically resembling spin or charge solitons in polyacetylene, and protected as the edges of hidden one-dimensional weak Chern insulators characterized by a zero-dimensional class-A topological invariant, solves experimental puzzles observed in R2Ir2O7 with rare-earth elements R. The domain wall realizes a novel quantum confinement of electrons and embosses a net uniform magnetization that enables magnetic control of electronic interface transports beyond the semiconductor paradigm.

We develop a variational Monte Carlo (VMC) method for electron-phonon coupled systems. The VMC method has been extensively used for investigating strongly correlated electrons over the last decades. However, its applications to electron-phonon coupled systems have been severely restricted because of its large Hilbert space. Here, we propose a variational wave function with a large number of variational parameters, which is suitable and tractable for systems with electron-phonon coupling. In the proposed wave function, we implement an unexplored electron-phonon correlation factor, which takes into account the effect of the entanglement between electrons and phonons. The method is applied to systems with diagonal electron-phonon interactions, i.e., interactions between charge densities and lattice displacements (phonons). As benchmarks, we compare VMC results with previous results obtained by the exact diagonalization, the Green function Monte Carlo method and the density matrix renormalization group for the Holstein and Holstein-Hubbard model. From these benchmarks, we show that the present method offers an efficient way to treat strongly coupled electron-phonon systems.

Exploiting the two-point measurement statistics, we propose a quantum measurement scheme of current with limited resolution of electron counting. Our scheme is equivalent to the full counting statistics in the long-time measurement with the ideal resolution, but is theoretically extended to take into account the resolution limit of actual measurement devices. Applying our scheme to a resonant level model, we show that the limited resolution of current measurement gives rise to a positive excess noise, which leads to a deviation from the Johnson-Nyquist relation. The deviation exhibits universal single-parameter scaling with the scaling variable Q = S-M/S-0, which represents the degree of the insufficiency of the resolution. Here, S-0 is the intrinsic noise, and S-M is the positive quantity that has the same dimension as S-0 and is defined solely by the measurement scheme. For the lack of the ideal resolution, the deviation emerges for Q < 1 as 2 exp[-(2 pi)(2)/Q] having an essential singularity at Q = 0, which followed by the square root dependence root Q/4 pi for Q >> 1. Our findings offer an explanation for the anomalous enhancement of noise temperature observed in Johnson noise thermometry.

© 2014 American Physical Society. The doped Hubbard model is a simple model for high-Tc cuprate superconductors, while its ground state remains a challenge. Here, by performing state-of-the-art variational Monte Carlo calculations for the strong-coupling Hubbard model, we find evidence that the d-wave superconducting phase emerges always near the phase separation region and the superconducting order has one-to-one correspondence with the enhancement of charge compressibility. The order as well as the phase separation are vulnerable to realistic intersite Coulomb interaction, while the superexchange interaction enhances both. An appropriate combination of these two widens the stable superconducting phase.

We present a quantum Monte Carlo study for Heisenberg spin-1/2 two-leg ladder systems doped with nonmagnetic impurities. The simulations are applied to the doped spin-ladder compound Sr(Cu1-x Zn-x)(2)O-3, where a large broadening of the Cu-65 NMR lines has been observed in experiment at low temperatures but far above the Neel temperature. We find that interladder couplings with a sizable coupling in the stacking direction are required to describe the line broadening, which cannot be explained by considering a single ladder only. Around a single impurity, spin correlations cause an exponentially decaying antiferromagnetic local magnetization in a magnetic field. We develop an effective model for the local magnetization of systems with many randomly distributed impurities, with few parameters which can be extracted out of quantum Monte Carlo calculations with a single impurity. The broadening arises from a drag effect, where the magnetization around an impurity works as an effective field for spins on the neighboring ladders, causing a nonexponentially decaying magnetization cloud around the impurity. Our results show that even for impurity concentrations as small as x = 0.001 and x = 0.0025, the broadening effect is large, in good quantitative agreement with experiment. We also develop a simple model for the effective interaction of two impurity spins.

Particularly in Sr2IrO4, the interplay between spin-orbit coupling, bandwidth and on-site Coulomb repulsion stabilizes a J(eff) = 1/2 spin-orbital entangled insulating state at low temperatures. Whether this insulating phase is Mott- or Slater-type, has been under intense debate. We address this issue via spatially resolved imaging and spectroscopic studies of the Sr2IrO4 surface using scanning tunneling microscopy/spectroscopy (STM/S). STS results clearly illustrate the opening of an insulating gap (150 similar to 250 meV) below the Neel temperature (T-N), in qualitative agreement with our density-functional theory (DFT) calculations. More importantly, the temperature dependence of the gap is qualitatively consistent with our DFT 1 dynamical mean field theory (DMFT) results, both showing a continuous transition from a gapped insulating ground state to a non-gap phase as temperatures approach TN. These results indicate a significant Slater character of gap formation, thus suggesting that Sr2IrO4 is a uniquely correlated system, where Slater and Mott-Hubbard-type behaviors coexist.

We reveal the full energy-momentum structure of the pseudogap of underdoped high-T-c cuprate superconductors. Our combined theoretical and experimental analysis explains the spectral-weight suppression observed in the B-2g Raman response at finite energies in terms of a pseudogap appearing in the single-electron excitation spectra above the Fermi level in the nodal direction of momentum space. This result suggests an s-wave pseudogap (which never closes in the energy-momentum space), distinct from the d-wave superconducting gap. Recent tunneling and photoemission experiments on underdoped cuprates also find a natural explanation within the s-wave pseudogap scenario.

We show that a wide class of unconventional quantum criticality emerges when orbital currents cause quantum phase transitions from zero-gap semiconductors such as Dirac fermions to a topological insulator or a Chern insulator. Changes in Fermi-surface topology concomitant with [SU(2) or time-reversal] symmetry breakings generate quantum critical lines (QCLs) even beyond the quantum critical point. This QCL running at temperature T = 0 separates two distinct topological phases. This is in contrast to the simple termination of the finite-temperature critical line at the quantum critical point without any extension of it at T = 0. Topology change causes the unconventionality beyond the concept of simple spontaneous symmetry breaking assumed in the conventional Landau-Ginzburg-Wilson scenario. The unconventional universality implied by mean-field critical exponents beta > 1/2 and delta < 3 is protected by the existence of the quantum critical line. It emerges for several specific lattice models including the honeycomb, kagome, diamond, and pyrochlore lattices. We also clarify phase diagrams of the topological phases in these lattices at finite temperatures.

Derivation of low-energy effective models by a partial trace summation of the electronic degrees of freedom far away from the Fermi level, called downfolding, is reexamined. We propose an improved formalism free from the double counting of electron correlation in the low-energy degrees of freedom. In this approach, the exchange-correlation energy in the local-density approximation (LDA) is replaced with the GW self-energy; herewith its low-energy part associated with the double counting is subtracted. Moreover, in our formalism, the frequency dependence of the effective parameter is renormalized into the static one. We apply the formalism to SrVO3 as well as to two iron-based superconductors, FeSe and FeTe. The resultant bandwidths of the effective models are nearly the same as those of the previous downfolding formalism because of striking cancellations between an increase arising from the exclusion of the low-energy correlation and a shrinking arising from the renormalization of the frequency dependence. In the nondegenerate multiband materials such as FeSe and FeTe, the momentum dependent self-energy effects yield substantial modifications of the band structures and relative shifts of orbital-energy levels of the effective models, which may explain the stability of the bicollinear antiferromagnetic phase in FeTe as well as the experimental absence of the antiferromagnetic phase in FeSe.

We present a quantum Monte Carlo study for Heisenberg spin-12 two-leg ladder systems doped with nonmagnetic impurities. The simulations are applied to the doped spin-ladder compound Sr(Cu1-xZnx)2O3, where a large broadening of the 65Cu NMR lines has been observed in experiment at low temperatures but far above the Néel temperature. We find that interladder couplings with a sizable coupling in the stacking direction are required to describe the line broadening, which cannot be explained by considering a single ladder only. Around a single impurity, spin correlations cause an exponentially decaying antiferromagnetic local magnetization in a magnetic field. We develop an effective model for the local magnetization of systems with many randomly distributed impurities, with few parameters which can be extracted out of quantum Monte Carlo calculations with a single impurity. The broadening arises from a drag effect, where the magnetization around an impurity works as an effective field for spins on the neighboring ladders, causing a nonexponentially decaying magnetization cloud around the impurity. Our results show that even for impurity concentrations as small as x=0.001 and x=0.0025, the broadening effect is large, in good quantitative agreement with experiment. We also develop a simple model for the effective interaction of two impurity spins. © 2013 American Physical Society.

Derivation of low-energy effective models by a partial trace summation of the electronic degrees of freedom far away from the Fermi level, called downfolding, is reexamined. We propose an improved formalism free from the double counting of electron correlation in the low-energy degrees of freedom. In this approach, the exchange-correlation energy in the local-density approximation (LDA) is replaced with the GW self-energy; herewith its low-energy part associated with the double counting is subtracted. Moreover, in our formalism, the frequency dependence of the effective parameter is renormalized into the static one. We apply the formalism to SrVO3 as well as to two iron-based superconductors, FeSe and FeTe. The resultant bandwidths of the effective models are nearly the same as those of the previous downfolding formalism because of striking cancellations between an increase arising from the exclusion of the low-energy correlation and a shrinking arising from the renormalization of the frequency dependence. In the nondegenerate multiband materials such as FeSe and FeTe, the momentum dependent self-energy effects yield substantial modifications of the band structures and relative shifts of orbital-energy levels of the effective models, which may explain the stability of the bicollinear antiferromagnetic phase in FeTe as well as the experimental absence of the antiferromagnetic phase in FeSe. © 2013 American Physical Society.

Recent theoretical studies on the origin of the pseudogap emerging in underdoped cuprate superconductors are overviewed, based on insights obtained by a cluster extension of the dynamical mean field theory (cDMFT) for the doped two-dimensional (2D) Mott insulator. The pseudogap obtained in the cDMFT shows an s-wave-like full-gap structure, distinct from the d-wave superconducting gap. The zero-temperature electronic structure supports that a non-Fermi liquid phase exists and underlies the pseudogap. The non-Fermi liquid phase is separated from the larger-doped Fermi liquid by topological transitions of the Fermi surface and an emergence of zeros of Green's function. A coexisting evolution of the poles (Fermi surface) and zeros of the Green's function is a unique feature of the pseudogap phase. The spectra well reproduce the arc/pocket formation, together with basic experimental properties of the pseudogap phase in the cuprates. Furthermore, a full-gap structure is supported by a comparison with the results of Raman experiments. The overall feature supports the proximity of the Mott insulator and the significance of the quantum criticality of the Mott transition. These numerical results are further favorably interpreted by extending the exciton concept, known in semiconductors, to doped Mott insulators. In this composite fermion (CF) theory, the pseudogap emerges as a gap arising from a hybridization of the quasiparticle (QP) with the CF. The pairing channel opening between a QP and a CF solves the puzzle of the dichotomy between the d-wave superconductivity and the precursory insulating gap in the same antinodal region. A mechanism of superconductivity emerges from this pairing.

We revisit the accuracy of the variational Monte Carlo (VMC) method by taking an example of ground state properties for the one-dimensional Hubbard model. We start from the variational wave functions with the Gutzwiller and long-range Jastrow factor introduced by Capello et al. [Phys. Rev. B 72, 085121 (2005)] and further improve it by considering several quantum-number projections and a generalized one-body wave function. We find that the quantum spin projection and total momentum projection greatly improve the accuracy of the ground state energy within 0.5% error, for both small and large systems at half filling. Besides, the momentum distribution function n(k) at quarter filling calculated up to 196 sites allows us direct estimate of the critical exponents of the charge correlations from the power-law behavior of n(k) near the Fermi wave vector. Estimated critical exponents well reproduce those predicted by the Tomonaga-Luttinger theory.

We present ab initio two-dimensional extended Hubbard-type multiband models for EtMe3Sb[Pd(dmit)(2)](2) (where dmit is 1,3-dithiole-2-thione-4,5-dithiolate) and kappa-(BEDT-TTF)(2)Cu(NCS)(2) [where BEDT-TTF is bis(ethylenedithio)-tetrathiafulvalene] after a downfolding scheme based on the constrained random-phase approximation (cRPA) and maximally localized Wannier orbitals, together with the dimensional downfolding. In the Pd(dmit)(2) salt, the antibonding state of the highest occupied molecular orbital (HOMO) and the bonding/antibonding states of the lowest unoccupied molecular orbital (LUMO) are considered to be the orbital degrees of freedom, while, in the kappa-BEDT-TTF salt, the HOMO-antibonding/bonding states are considered. Accordingly, a three-band model for the Pd(dmit)(2) salt and a two-band model for the kappa-(BEDT-TTF) salt are derived. We derive single-band models for the HOMO-antibonding state for both of the compounds as well. The HOMO antibonding band of the Pd(dmit)(2) salt has a triangular structure of the transfers with a one-dimensional anisotropy, in contrast to the nearly equilateral triangular structure predicted in the extended Huuckel results. The ratio of the larger interchain transfer t(b) to the intrachain transfer t(a) is around t(b)/t(a) similar to 0.82. Our calculated screened onsite interaction U and the largest offsite interaction V are similar to 0.7 and similar to 0.23 eV, respectively, for EtMe3Sb[Pd(dmit)(2)](2) and similar to 0.8 and similar to 0.2 eV for kappa-(BEDT-TTF)(2)Cu(NCS)(2). These values are large enough compared to transfers t as similar to 55 meV for the Pd(dmit)(2) salt and similar to 65 meV for the kappa-BEDT-TTF one, and the resulting large correlation strength (U-V)/t similar to 10 indicates that the present compounds are classified as the strongly correlated electron systems. In addition, the validity whether the present multiband model can be reduced to the single-band model for the HOMO-antibonding state, widely accepted in the literature, is discussed. For this purpose, we estimated the order of vertex corrections ignored in the cRPA downfolding to the single-band model, which is given by W'/D, where W' is a full-screened-interaction matrix element between the HOMO-antibonding and other bands away from the Fermi level (namely, HOMO-bonding or LUMO-bonding/antibonding bands), whereas D is the energy distance between the Fermi level and the bands away from the Fermi level. In the present materials, W'/D estimated as 0.3-0.5 signals a substantial correction and thus the exchange process between the low-energy HOMO-antibonding and other bands away from the Fermi level may play a key role to the low-energy ground state. This supports that the minimal models to describe the low-energy phenomena of the organic compounds are the multiband models and may not be reduced to the single-band model.

A two-dimensional superconductor (SC) on surfaces of topological insulators (TIs) is a mixture of s-wave and helical p-wave components when induced by s-wave interactions, since spin and momentum are correlated. On the basis of the Abrikosov-Gor'kov theory, we reveal that unconventional SCs on the surfaces of TIs are stable against time-reversal symmetric (TRS) impurities within a region of small impurity concentration. Moreover, we analyze the stability of the SC on the surfaces of TIs against impurities beyond the perturbation theory by solving the real-space Bogoliubov-de Gennes equation for an effective tight-binding model of a TI. We find that the SC is stable against strong TRS impurities. The behaviors of bound states around an impurity suggest that the SC on the surfaces of TIs is not a topological SC.

We develop a multiscale ab initio scheme for correlated electrons (MACE) for transition-metal-oxide heterostructures, and determine the parameters of the low-energy effective model. By separating Ti t(2g) bands near the Fermi level from the global Kohn-Sham (KS) bands of LaAlO3 (LAO)/SrTiO3 (STO), which are highly entangled with each other, we are able to calculate the parameters of the low-energy effective model of the interface with the help of constrained random phase approximation (cRPA). The on-site energies of the Ti t(2g) orbitals in the 1st layer is about 650 meV lower than those in the second layer. In the 1st layer, the transfer integral of the Ti t(2g) orbital is nearly the same as that of bulk STO, while the effective screened Coulomb interaction becomes about 10% larger than that of bulk STO. The differences in the parameters from bulk STO decrease rapidly with increasing distance from the interface. Our present versatile method enables us to derive effective ab initio low-energy models and to study interfaces of strongly correlated electron systems from first principles.

A scheme to incorporate nonlocal polarizations into the dynamical mean-field theory (DMFT) and a tailormade way to determine the effective interaction for DMFT are systematically investigated. Applying it to the two-dimensional Hubbard model, we find that nonlocal polarizations induce a nontrivial filling-dependent antiscreening effect for the effective interaction. The present scheme combined with density functional theory offers an ab initio way to derive effective on-site interactions for the impurity problem in DMFT. We apply it to SrVO3 and find that the antiscreening competes with the screening caused by the off-site interaction.

We present an ab initio analysis with density functional theory for superconductors (SCDFT) to understand the superconducting mechanism of doped layered nitrides beta-LixMNCl (M = Ti, Zr, and Hf). The current version of SCDFT is based on the Migdal-Eliashberg theory and has been shown to reproduce accurately experimental superconducting-transition temperatures T-c of a wide range of phonon-mediated superconductors. In the present case, however, our calculated T-c <= 4.3 K (M = Zr) and <= 10.5 K (M = Hf) are found to be less than half of the experimental T-c. In addition, T-c obtained in the present calculation increases with increasing doping concentration x, opposite to that observed in the experiment. Our results indicate that we need to consider some factors missing in the current SCDFT based on the Migdal-Eliashberg theory.

A scheme to incorporate nonlocal polarizations into the dynamical mean-field theory (DMFT) and a tailor-made way to determine the effective interaction for DMFT are systematically investigated. Applying it to the two-dimensional Hubbard model, we find that nonlocal polarizations induce a nontrivial filling-dependent antiscreening effect for the effective interaction. The present scheme combined with density functional theory offers an ab initio way to derive effective on-site interactions for the impurity problem in DMFT. We apply it to SrVO3 and find that the antiscreening competes with the screening caused by the off-site interaction. © 2012 American Physical Society.

We predict that iron-based superconductors discovered near d(6) configuration (5 Fe 3d orbitals filled by 6 electrons) is located on the foot of an unexpectedly large dome of correlated electron matter centered at the Mott insulator at d(5) (namely, half filling). This is based on the many-variable variational Monte Carlo results for ab initio low-energy models derived by the downfolding. The d(5) Mott proximity extends to subsequent emergence of incoherent metals, orbital differentiations due to the Mott physics, and Hund's rule coupling, followed by antiferromagnetic quantum criticality, in quantitative accordance with available experiments.

We present an ab initio analysis for the ground-state properties of a correlated organic compound kappa-(BEDT-TTF)(2)Cu(NCS)(2). First, we derive an effective two-dimensional low-energy model from first principles, having short-ranged transfers and short-ranged Coulomb and exchange interactions. Then, we perform many-variable variational Monte Carlo calculations for this model and draw a ground-state phase diagram as functions of scaling parameters for the onsite and off-site interactions. The phase diagram consists of three phases; a paramagnetic metallic phase, an antiferromagnetic (Mott) insulating phase, and a charge-ordered phase. In the phase diagram, the parameters for the real compound are close to the first-order Mott transition, being consistent with experiments. We show that the off-site Coulomb and exchange interactions affect the phase boundary; (i) they appreciably stabilize the metallic state against the Mott insulating phase and (ii) enhance charge fluctuations in a wide parameter region in the metallic phase. We observe arc-like structure in Fermi surface around the region where the charge fluctuations are enhanced. Possible relevance of the charge fluctuations to the experimentally observed dielectric anomaly in the kappa-BEDT-TTF family compounds is also pointed out.

Ab initio analyses of A(2)IrO(4) (A = Sr; Ba) are presented. Effective Hubbard-type models for Ir 5d t(2g) manifolds downfolded from the global band structure are solved based on the dynamical mean-field theory. The results for A Sr and Ba correctly reproduce paramagnetic metals undergoing continuous transitions to insulators below the Neel temperature T-N. These compounds are classified not into Mott insulators but into Slater insulators. However, the insulating gap opens by a synergy of the Neel order and significant band renormalization, which is also manifested by a 2D bad metallic behavior in the paramagnetic phase near the quantum criticality.

We examine the cluster-size dependence of the cellular dynamical mean-field theory (CDMFT) applied to the two-dimensional Hubbard model. Employing the continuous-time quantum Monte Carlo method as the solver for the effective cluster model, we obtain CDMFT solutions for 4-, 8-, 12-, and 16-site clusters at a low temperature. Comparing various periodization schemes, which are used to construct the infinite-lattice quantities from the cluster results, we find that the cumulant periodization yields the fastest convergence for the hole-doped Mott insulator where the most severe size dependence is expected. We also find that the convergence is much faster around (0,0) and (pi/2, pi/2) than around (pi, 0) and (pi, pi). The cumulant-periodized self-energy seems to be close to its thermodynamic limit already for a 16-site cluster in the range of parameters studied. The 4-site results remarkably agree well with the 16-site results, indicating that the previous studies based on the 4-site cluster capture the essence of the physics of doped Mott insulators.

We present ab initio two-dimensional extended Hubbard-type multiband models for EtMe 3Sb[Pd(dmit) 2] 2 (where dmit is 1,3-dithiole-2-thione-4,5-dithiolate) and κ-(BEDT-TTF) 2Cu(NCS) 2 [where BEDT-TTF is bis(ethylenedithio)-tetrathiafulvalene] after a downfolding scheme based on the constrained random-phase approximation (cRPA) and maximally localized Wannier orbitals, together with the dimensional downfolding. In the Pd(dmit) 2 salt, the antibonding state of the highest occupied molecular orbital (HOMO) and the bonding/antibonding states of the lowest unoccupied molecular orbital (LUMO) are considered to be the orbital degrees of freedom, while, in the κ-BEDT-TTF salt, the HOMO-antibonding/bonding states are considered. Accordingly, a three-band model for the Pd(dmit) 2 salt and a two-band model for the κ-(BEDT-TTF) salt are derived. We derive single-band models for the HOMO-antibonding state for both of the compounds as well. The HOMO antibonding band of the Pd(dmit) 2 salt has a triangular structure of the transfers with a one-dimensional anisotropy, in contrast to the nearly equilateral triangular structure predicted in the extended Hückel results. The ratio of the larger interchain transfer t b to the intrachain transfer t a is around t b/t a∼0.82. Our calculated screened onsite interaction U and the largest offsite interaction V are ∼0.7 and ∼0.23 eV, respectively, for EtMe 3Sb[Pd(dmit) 2] 2 and ∼0.8 and ∼0.2 eV for κ-(BEDT-TTF) 2Cu(NCS) 2. These values are large enough compared to transfers t as ∼55 meV for the Pd(dmit) 2 salt and ∼65 meV for the κ-BEDT-TTF one, and the resulting large correlation strength (U-V)/t∼10 indicates that the present compounds are classified as the strongly correlated electron systems. In addition, the validity whether the present multiband model can be reduced to the single-band model for the HOMO-antibonding state, widely accepted in the literature, is discussed. For this purpose, we estimated the order of vertex corrections ignored in the cRPA downfolding to the single-band model, which is given by W′/D, where W′ is a full-screened-interaction matrix element between the HOMO-antibonding and other bands away from the Fermi level (namely, HOMO-bonding or LUMO-bonding/antibonding bands), whereas D is the energy distance between the Fermi level and the bands away from the Fermi level. In the present materials, W′/D estimated as 0.3-0.5 signals a substantial correction and thus the exchange process between the low-energy HOMO-antibonding and other bands away from the Fermi level may play a key role to the low-energy ground state. This supports that the minimal models to describe the low-energy phenomena of the organic compounds are the multiband models and may not be reduced to the single-band model. © 2012 American Physical Society.

Underdoped Mott insulators provide us with a challenge of many-body physics. Recent renewed understanding is discussed in terms of the evolution of pole and zero structure of the single-particle Green's function. Pseudogap as well as Fermi arc/pocket structure in the underdoped cuprates is well reproduced from the recent cluster extension of the dynamical mean-field theory. Emergent coexisting zeros and poles set the underdoped Mott insulator apart from the Fermi liquid, separated by topological transitions. The cofermion proposed as a generalization of exciton in the slave-boson framework accounts for the origin of the zero surface formation. The cofermion-quasiparticle hybridization gap offers a natural understanding of the pseudogap and various unusual Mottness. Furthermore the cofermion offers a novel pairing mechanism, where the cofermion has two roles: It reinforces the Cooper pair as a pair partner of the quasiparticle and acts as a glue as well. It provides a strong insight for solving the puzzle found in the dichotomy of the gap structure. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Superconductivity on the surface of topological insulators is known to be anisotropic and unconventional in that the symmetry is the mixture of s-wave and nodeless p-wave component under certain conditions. In contrast to Anderson's theorem for the insensitivity of the s-wave superconducting critical temperature to the nonmagnetic (time-reversal symmetric (TRS)) impurities, anisotropic superconductors including nodeless p-wave one are in general fragile even with small concentration of the TRS impurities. By employing the Abrikosov-Gor'kov theory, we clarify that this type of unconventional superconductivity emergent on the surface state of the strong topological insulators robustly survive against TRS impurities.

We study pseudogap phenomena and Fermi-arc formation experimentally observed in typical two-dimensional doped Mott insulators, namely, underdoped cuprate superconductors. To develop a physically unequivocal theory, we start from the slave-boson mean-field theory for the Hubbard model on a square lattice. Our crucial step is to further take into account the charge dynamics and fluctuations. The extra charge fluctuations seriously modify low-energy single-particle spectra of doped Mott insulators near the Fermi level: An electron added around an empty site (or a hole added around a doubly occupied site) constitutes composite fermion (cofermion), called holo-electron (or doublo-hole) at low energy in distinction from the normal quasiparticles. These unexplored composite fermions substantiate the extra charge fluctuation. We show that the quasiparticles hybridize with the holo-electrons and doublo-holes. The resultant hybridization gap is identified as the pseudogap observed in the underdoped region of the high-T-c cuprates. Because the Fermi level crosses the top (bottom) of the low-energy band formed just below (above) the hybridization gap in the hole-doped (electron-doped) case, it causes a Fermi-surface reconstruction, namely, a topological change in the Fermi surface forced by the penetration of zeros of the quasiparticle Green's function. This reconstruction signals the emergence of a non-Fermi-liquid phase. The pseudogap and the resultant formation of pocket or arc of the Fermi surface reproduce the experimental results for the cuprate superconductors in the underdoped region. The pairing channel opens not only between two quasiparticles, but also between a quasiparticle and a cofermion. This pairing solves the puzzle of the dichotomy between the d-wave superconductivity and the precursors of the the insulating gap in the antinodal region. We propose and analyze them as the mechanism of the high-temperature superconductivity for the cuprates.

We study pseudogap phenomena and Fermi-arc formation experimentally observed in typical two-dimensional doped Mott insulators, namely, underdoped cuprate superconductors. To develop a physically unequivocal theory, we start from the slave-boson mean-field theory for the Hubbard model on a square lattice. Our crucial step is to further take into account the charge dynamics and fluctuations. The extra charge fluctuations seriously modify low-energy single-particle spectra of doped Mott insulators near the Fermi level: An electron added around an empty site (or a hole added around a doubly occupied site) constitutes composite fermion (cofermion), called holo-electron (or doublo-hole) at low energy in distinction from the normal quasiparticles. These unexplored composite fermions substantiate the extra charge fluctuation. We show that the quasiparticles hybridize with the holo-electrons and doublo-holes. The resultant hybridization gap is identified as the pseudogap observed in the underdoped region of the high-Tc cuprates. Because the Fermi level crosses the top (bottom) of the low-energy band formed just below (above) the hybridization gap in the hole-doped (electron-doped) case, it causes a Fermi-surface reconstruction, namely, a topological change in the Fermi surface forced by the penetration of zeros of the quasiparticle Green's function. This reconstruction signals the emergence of a non-Fermi-liquid phase. The pseudogap and the resultant formation of pocket or arc of the Fermi surface reproduce the experimental results for the cuprate superconductors in the underdoped region. The pairing channel opens not only between two quasiparticles, but also between a quasiparticle and a cofermion. This pairing solves the puzzle of the dichotomy between the d-wave superconductivity and the precursors of the the insulating gap in the antinodal region. We propose and analyze them as the mechanism of the high-temperature superconductivity for the cuprates. © 2011 American Physical Society.

We study roles of electron correlations on topological insulators or quantum spin Hall insulators on honeycomb lattice with spin-orbit interaction. Accurate variationalMonteCarlo calculations with a large number of variational parameters show that the increasing on-site Coulomb interactions cause a strong suppression of the charge Drude weight in the helical-edge metallic states leading to a presumable Mott transition (or strong crossover) from a conventional topological insulator to an edge Mott insulator before a transition to a bulk antiferromagnetic insulator. The intermediate bulk-topological and edge-Mott-insulator phase has a helical spin-liquid character with time-reversal symmetry.

We study an extended Hubbard model with the nearest-neighbor Coulomb interaction on the pyrochlore lattice at half filling. An interaction-driven insulating phase with nontrivial Z(2) invariants emerges at the Hartree-Fock mean-field level in the phase diagram. This topological insulator phase competes with other ordered states and survives in a parameter region surrounded by a semimetal, antiferromagnetic and charge ordered insulators. The symmetries of these phases are group-theoretically analyzed. We also show that the ferromagnetic interaction enhances the stability of the topological phase.

By using a variational Monte Carlo method, we examine an effective low-energy model for LaFeAsO derived from an ab initio downfolding scheme. We show that quantum and many-body fluctuations near the antiferromagnetic (AF) quantum critical point largely reduce the antiferromagnetic ordered moment. Our derived model not only quantitatively reproduces the small ordered moment in LaFeAsO, but also accounts for the diversity from LaFePO, BaFe2As2 to FeTe. Electron correlation is found to determine the observed material dependence. We also find that LaFeAsO is subject to large orbital fluctuations, sandwiched by the AF Mott insulator and weakly correlated metals. The orbital fluctuations and Dirac-cone dispersion hold keys for the diverse magnetic properties.

We propose that an extension of the exciton concept to doped Mott insulators offers a fruitful insight into challenging issues of the copper oxide superconductors. In our extension, new fermionic excitations called cofermions emerge in conjunction to generalized excitons. The cofermions hybridize with conventional quasiparticles. Then a hybridization gap opens, and is identified as the pseudogap observed in the underdoped cuprates. The resultant Fermi-surface reconstruction naturally explains a number of unusual properties of the underdoped cuprates, such as the Fermi arc and/or pocket formation.

An ab initio downfolding method is formulated to construct low-dimensional models for correlated electrons. In addition to band downfolding by a constrained random phase approximation formulated for 3D models, screening away from the target layer (chain) is further involved. Eliminating the off-target degrees of freedom, namely, dimensional downfolding, yields ab initio low-dimensional models. The method is applied to derive a 2D model for the layered superconductor LaFeAsO, where interlayer screening crucially makes the effective interaction short-ranged and reduces the onsite Coulomb interactions by 10-20% compared with the 3D model for the five iron-3d orbitals.

We present a theory of the DC electron transport in insulators near Anderson-Mott transitions under the influence of coexisting electron correlation and randomness. At sufficiently low temperatures, the DC electron transport in Anderson-Mott insulators is determined by the single-particle density of states (DOS) near the Fermi energy (E-F). Anderson insulators, caused by randomness, are characterized by a nonzero DOS at E-F. However, recently, the authors proposed that coexisting randomness and short-ranged interaction in insulators open a soft Hubbard gap in the DOS, and the DOS vanishes only at E-F. Based on the picture of the soft Hubbard gap, we derive a formula for the critical behavior for the temperature dependence of the DC resistivity. Comparisons of the present theory with experimental results of electrostatic carrier doping into an organic conductor kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Br demonstrate the evidence for the present soft-Hubbard scaling.

Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries and characterizations of strongly correlated electron materials and by requirements for understanding mechanisms of intriguing phenomena beyond a single-particle picture. A three-stage scheme is developed as renormalized multi-scale solvers (RMS) utilizing the hierarchical electronic structure in the energy space. It provides us with an ab initio downfolding of the global band structure into low-energy effective models followed by low-energy solvers for the models. The RMS method is illustrated with examples of several materials. In particular, we overview cases such as dynamics of semiconductors, transition metals and their compounds including iron-based superconductors and perovskite oxides, and organic conductors of kappa-ET type.

We study electronic structure of hole- and electron-doped Mott insulators in the two-dimensional Hubbard model to reach a unified picture for the normal state of cuprate high-T-c superconductors. By using a cluster extension of the dynamical mean-field theory, we demonstrate that structure of coexisting zeros and poles of the single-particle Green's function holds the key to understand Mott physics in the underdoped region. We show evidence for the emergence of non-Fermi-liquid phase caused by the topological quantum phase transition of Fermi surface by analyzing low-energy charge dynamics. The spectra calculated in a wide range of energy and momentum reproduce various anomalous properties observed in experiments for the high-T-c cuprates. Our results reveal that the pseudogap in hole-doped cuprates has a d-wavelike structure only below the Fermi level while it retains non-d-wave structure with a fully opened gap above the Fermi energy even in the nodal direction due to a zero surface extending over the entire Brillouin zone. In addition to the non-d-wave pseudogap, the present comprehensive identifications of the spectral asymmetry as to the Fermi energy, the Fermi arc, and the back-bending behavior of the dispersion, waterfall, and low-energy kink, in agreement with the experimental anomalies of the cuprates, do not support that these originate from (the precursors of) symmetry breakings such as the preformed pairing and the d-density-wave fluctuations, but support that they are direct consequences of the proximity to the Mott insulator. Several possible experiments are further proposed to prove or disprove our zero mechanism.

We study a three-dimensional Anderson-Hubbard model under the coexistence of short-range interaction and diagonal disorder within the Hartree-Fock approximation. We show that the density of states at the Fermi energy is suppressed in the metallic phases near the metal-insulator transition as a proximity effect of the soft Hubbard gap in the insulating phases. The transition to the insulator is characterized by a vanishing density of states (DOS) in contrast to the formation of a quasiparticle peak at the Fermi energy obtained using the dynamical mean field theory in pure systems. Furthermore, we show that there exist frozen spin moments in the paramagnetic metal.

The role of electronic Coulomb correlations in iron-based superconductors is an important open question. We provide theoretical evidence for strong correlation effects in FeSe, based on dynamical mean field calculations. Our ab initio spectral properties first demonstrate the existence of a lower Hubbard band. Moreover, together with significant orbital-dependent mass enhancements, we find that the normal state is a bad metal over an extended temperature range, implying a non-Fermi liquid due to formation of local moments. Predictions for angle-resolved photoemission spectroscopy are made.

Motivated by a recent experiment on volborthite, a typical spin-1/2 antiferromagnet with a kagome lattice structure, we study the magnetization process of a classical Heisenberg model on a spatially distorted kagome lattice using the Monte Carlo (MC) method. We find a distortion-induced magnetization step at low temperatures and low magnetic fields. The magnitude of this step is given by Delta m(z) = vertical bar 1 - alpha vertical bar/3 alpha at zero temperature, where alpha denotes the spatial anisotropy in exchange constants. The magnetization step signals a first-order transition at low temperatures, between two phases distinguished by distinct and well-developed short-range spin correlations, one characterized by spin alignment of a local 120 degrees structure with a root 3 x root 3 period, and the other by a partially spin-flopped structure. We point out the relevance of our results to the unconventional steps observed in volborthite.

We analyze and overview some of the different types of unconventional quantum criticalities by focusing on two origins. One origin of the unconventionality is the proximity to first-order transitions. The border between the first-order and continuous transitions is described by a quantum tricritical point (QTCP) for symmetry breaking transitions. One of the characteristic features of the quantum tricriticality is the concomitant divergence of an order parameter and uniform fluctuations, in contrast to the conventional quantum critical point (QCP). The interplay of these two fluctuations generates unconventionality. Several puzzling non-Fermi-liquid properties in experiments are taken to be accounted for by the resultant universality, as in the cases of YbRh2Si2, CeRu2Si2 and beta-YbAlB4. Another more dramatic unconventionality appears again at the border of the first-order and continuous transitions, but in this case for topological transitions such as metal-insulator and Lifshitz transitions. This border, the marginal quantum critical point (MQCP), belongs to an unprecedented universality class with diverging uniform fluctuations at zero temperature. The Ising universality at the critical end point of the first-order transition at nonzero temperatures transforms to the marginal quantum criticality when the critical temperature is suppressed to zero. The MQCP has a unique feature with a combined character of symmetry breaking and topological transitions. In the metal-insulator transitions, the theoretical results are supported by experimental indications for V2-xCrxO3 and an organic conductor kappa-(ET)(2)Cu[N(CN)(2)] Cl. Identifying topological transitions also reveals how non-Fermi liquid appears as a phase in metals. The theory also accounts for the criticality of a metamagnetic transition in ZrZn2, by interpreting it as an interplay of Lifshitz transition and correlation effects. We discuss the common underlying physics in these examples.

Effective low-energy Hamiltonians for several different families of iron-based superconductors are compared after deriving them from the downfolding scheme based on first-principles calculations. Systematic dependences of the derived model parameters on the families are elucidated, many of which are understood from the systematic variation of the covalency between Fe-3d and pnictogen-/chalcogen-p orbitals. First, LaFePO, LaFeAsO (1111), (BaFeAs2)-As-2 (122), LiFeAs (111), FeSe, and FeTe (11) have overall similar band structures near the Fermi level, where the total widths of 10-fold Fe-3d bands are mostly around 4.5 eV. However, the derived effective models of the 10-fold Fe-3d bands (d model) for FeSe and FeTe have substantially larger effective onsite Coulomb interactions U similar to 4.2 and 3.4 eV, respectively, after the screening by electrons on other bands and after averaging over orbitals, as compared to similar to 2.5 eV for LaFeAsO. The difference is similar in the effective models containing p orbitals of As, Se or Te (dp or dpp model), where U ranges from similar to 4 eV for the 1111 family to similar to 7 eV for the 11 family. The exchange interaction J has a similar tendency. The family dependence of models indicates a wide variation ranging from weak correlation regime (LaFePO) to substantially strong correlation regime (FeSe). The origin of the larger effective interaction in the 11 family is ascribed to smaller spread of the Wannier orbitals generating larger bare interaction, and to fewer screening channels by the other bands. This variation is primarily derived from the distance h between the pnictogen/chalcogen position and the Fe layer: The longer h for the 11 family generates more ionic character of the bonding between iron and anion atoms, while the shorter h for the 1111 family leads to more covalent-bonding character, the larger spread of the Wannier orbitals, and more efficient screening by the anion p orbitals. The screened interaction of the d model is strongly orbital dependent, which is also understood from the Wannier spread. The dp and dpp models show much weaker orbital dependence. The larger h also explains why the 10-fold 3d bands for the 11 family are more entangled with the smearing of the "pseudogap'' structure above the Fermi level seen in the 1111 family. While the family-dependent semimetallic splitting of the bands primarily consists of d(yz)/d(zx) and d(x2-y2) orbitals, the size of the pseudogap structure is controlled by the hybridization between these orbitals and d(xy)/d(3z2-r2): A large hybridization in the 1111 family generates a large "band-insulating''-like pseudogap ( hybridization gap), whereas a large h in the 11 family weakens them, resulting in a "half-filled'' like bands of orbitals. This may enhance strong correlation effects in analogy with Mott physics and causes the orbital selective crossover in the three orbitals. On the other hand, the geometrical frustration t'/t, inferred from the ratio of the next-nearest transfer t' to the nearest one t of the d model is relatively larger for the 1111 family than the 11 one. The models comprehensively derived here may serve as a firm starting basis of understanding both common and diverse properties of the iron-based superconductors including magnetism and superconductivity.

We propose a method of systematically controlling carrier densities at the interface of transition metal oxide heterostructures without introducing disorders. By inserting nonpolar layers sandwiched by polar layers, continuous carrier doping into the interface can be realized. This method enables us to control total carrier density per unit cell systematically up to high values on the order of unity.

We study two models realized by two-component Fermi gases loaded in optical lattices. We clarify that multiband effects inevitably caused by the optical lattices generate a rich structure, when the systems crossover from the region of weakly bound molecular bosons to the region of strongly bound atomic bosons. Here the crossover can be controlled by attractive fermion interaction. One of the present models is a case with attractive fermion interaction, where an insulator-superfluid transition takes place. The transition is characterized as the transition between a band insulator and a Bose-Einstein condensate superfluid state. Differing from the conventional Bardeen-Cooper-Schrieffer (BCS) superfluid transition, this transition shows unconventional properties. In contrast to the one-particle excitation gap scaled by the superfluid order parameter in the conventional BCS transition, because of the multiband effects, a large gap of one-particle density of states is retained all through the transition, although the superfluid order grows continuously from zero. A re-entrant transition with lowering temperature is another unconventionality. The other model is the case with coexisting attractive and repulsive interactions. Within a mean-field treatment, we find a new insulating state, an orbital ordered insulator. This insulator is one candidate for the Mott insulator of molecular bosons and is the first example that the orbital internal degrees of freedom of molecular bosons appears explicitly. Besides the emergence of a new phase, a coexisting phase also appears where superfluidity and an orbital order coexist just by doping holes or particles. The insulating and superfluid particles show differentiation in momentum space as in the high-T-c cuprate superconductors.

In a previous work [Phys. Rev. B 77, 085122 (2008)], a procedure for constructing low-energy models of electrons in solids was proposed. The procedure starts with dividing the Hilbert space into two subspaces: the low-energy part ("d space") and the rest of the space ("r space"). The low-energy model is constructed for the d space by eliminating the degrees of freedom of the r space. The thus derived model contains the strength of electron correlation expressed by a partially screened Coulomb interaction, calculated in the constrained random-phase approximation (cRPA), where screening channels within the d space, P-d, are subtracted. One conceptual problem of this established downfolding method is that for entangled bands it is not clear how to cut out the d space and how to distinguish P-d from the total polarization. Here, we propose a simple procedure to overcome this difficulty. The d space is defined to be an isolated set of bands generated from a set of maximally localized Wannier basis, which consequently defines P-d. The r subspace is constructed as the complementary space orthogonal to the d subspace, resulting in two sets of completely disentangled bands. Using these disentangled bands, the effective parameters of the d space are uniquely determined by the cRPA method. The method is successfully applied to 3d transition metals.

We clarify effects of zeros of the Green function on a Fermi arc and on a non-Fermi liquid behavior in the two-dimensional Hubbard model by means of the cellular dynamical mean-field theory (CDMFT). We study in detail the state with a hole-pocket Fermi surface and zeros of the Green function, which was found for a slightly doped Mott insulator in an earlier CDMFT calculation [T.D. Stanescu, G. Kotliar, Phys. Rev. B 74 (2006) 125110; T.D. Stanescu, M. Civelli, K. Haule, G. Kotliar, Ann. Phys. (N.Y.) 321 (2006) 1682]. As thermal or other extrinsic scatterings of electrons broaden the zeros, regions around the zero surface gain an imaginary part of the self-energy, which strongly suppresses the spectral intensity, especially on the closer side of the hole pocket to the zero surface. Then the rest emerges as a Fermi arc. Quasiparticle weight becomes ill defined on the closer side of the Fermi pocket while it is well defined on the opposite side, which means that a differentiation of electrons occurs in the momentum space, indicating an emergence of a non-Fermi liquid phase. (C) 2009 Elsevier B.V. All rights reserved.

Interplay of electron correlation and randomness is studied using the Anderson-Hubbard model within the Hartree-Fock (HF) approximation. Under the coexistence of short-range interaction and diagonal disorder, we obtain the ground-state phase diagram in three dimensions (3D), which includes an antiferromagnetic insulator, an antiferromagnetic metal, a paramagnetic insulator (Anderson-localized insulator), and a paramagnetic metal. Although only the short-range interaction is present in this model, we find unconventional soft gaps in the insulating phases irrespective of electron filling, spatial dimensions. and long-range order, where the single-particle density of states (DOS) vanishes with a power-law scaling in 1D or even faster in 2D and 3D toward the Fermi energy. We call such a gap a soft Hubbard gap. Moreover, exact-diagonalization results for 1D support the formation of a soft Hubbard gap beyond the mean-field level. The formation of the soft Hubbard gap cannot be attributed to the conventional theory by Efros and Shklovskii (ES) owing the emergence of soft gaps to the long-range Coulomb interaction. Indeed, on the basis of a multivalley energy landscape, we propose a phenomenological scaling theory, which predicts a scaling of the DOS, A in energy E as A(E) proportional to exp[-(-gamma log vertical bar E - E-F vertical bar)(d)]. Here, d is the spatial dimension, E-F is the Fermi energy, and gamma is a lion universal constant. This scaling is in perfect agreement with the numerical results. We further discuss a correction of the scaling, of the DOS by the long-range part of the Coulomb interaction, which modifies the ES scaling. Furthermore, explicit formulae for the temperature dependence of the DC resistivity via variable-range hopping under the influence of the soft gaps are derived. Finally, we compare the present theory with experimental results for SrRu1-xTixO3.

We derive effective Hubbard-type Hamiltonians of kappa-(BEDT-TTF)(2)X, using an ab initio downfolding technique, for the first time for organic conductors. They contain dispersions of the highest occupied Wannier-type molecular orbitals with the nearest neighbor transfer t similar to 0.067 eV for a metal X = Cu(NCS)(2) and 0.055 eV for a Mott insulator X = Cu-2(CN)(3), as well as screened Coulomb interactions. It shows unexpected differences from the conventional extended Huckel results, especially much stronger onsite interaction U similar to 0.8 eV (U/t similar to 12-15) than the Huckel estimates (U/t similar to 7-8) as well as an appreciable longer-ranged interaction. Reexamination on physics of this family of materials is required from this realistic basis.

We propose a phenomenological spin fluctuation theory for anti ferromagnetic quantum tricritical point (QTCP), where a first-order phase transition changes into a continuous transition at zero temperature. Under magnetic fields, ferromagnetic quantum critical fluctuations develop around the anti ferromagnetic QTCP in addition to antiferromagnetic fluctuations, which is in sharp contrast with the conventional anti ferromagnetic quantum critical point. For itinerant electron systems, we show that the temperature dependence of critical magnetic fluctuations around the QTCP is given as chi(Q) proportional to T-3/2 (chi(0) proportional to T-3/4) at the anti ferromagnetic ordering (ferromagnetic) wave number q = Q (q = 0). The convex temperature dependence of chi(-1)(0) is a characteristic feature of the QTCP, which has never been seen in the conventional spin fluctuation theory. We propose a general theory of quantum tricriticality that has nothing to do with the specific Kondo physics itself, and solves puzzles of quantum criticalities widely observed in heavy-fermion systems such as YbRh2Si2, CeRu2Si2, and beta-YbAlB4. For YbRh2Si2, our theory successfully reproduces quantitative behaviors of the experimentally obtained ferromagnetic susceptibility and magnetization curve when suitable phenomenological parameters are chosen. The quantum tricriticality is also consistent with singularities of other physical properties such as specific heat, nuclear magnetic relaxation time 1/T1T, and the Hall coefficient. For CeRu2Si2 and beta-YbAlB4, we point out that the quantum tricriticality is a possible origin of the anomalous diverging enhancement of the uniform susceptibility observed in these materials.

We theoretically study the stability of the solidified second-layer He-3 at 4/7 of the first-layer density adsorbed on graphite, which exhibits quantum spin liquid. We construct a lattice model for the second-layer He-3 by taking account of density fluctuations on the third layer together by employing the refined configuration recently found by path integral Monte Carlo simulations. When holes are doped into the 4/7 solid, within the mean field approximation, the density-ordered fluid emerges. The evolution of hole pockets offers a Unified explanation for the measured doping and temperature dependences of specific-heat anomalies. We argue that differentiation in momentum space is a key to understanding the physics and accounts for multiscale thermodynamic anomalies in the mono- and double-layered He-3 Systems beyond the mean-field level.

We study the evolution of metals from Mott insulators in the carrier-doped 2D Hubbard model using a cluster extension of the dynamical mean-field theory. While the conventional metal is simply characterized by the Fermi surface (pole of the Green function G), interference of the zero surfaces of G with the pole surfaces becomes crucial in the doped Mott insulators. Mutually interfering pole and zero surfaces are dramatically transferred over the Mott gap, when lightly doped holes synergetically loosen the doublon-holon binding. The heart of the Mott physics such as the pseudogap, hole pockets, Fermi arcs, in-gap states, Lifshitz transitions, and non-Fermi liquids appears as natural consequences of this global interference in the frequency space.

We study the Anderson-Hubbard model in the Hartree-Fock approximation and the exact diagonalization under the coexistence of short-range interaction and diagonal disorder. We show that there exist unconventional soft gaps, where the single-particle (SP) density of states (DOS) A follows a scaling in energy E as A(E)proportional to exp[-(-gamma log|E-E-F|)(d)] irrespective of electron filling and long-range order. Here, d is the spatial dimension, E-F the Fermi energy and gamma a nonuniversal constant. We propose a multivalley energy landscape as their origin. Possible experiments to verify the present theory are proposed.

Variational wave functions used in the variational Monte Carlo (VMC) method are extensively improved to overcome the biases coming from the assumed variational form of the wave functions. We construct a highly generalized variational form by introducing a large number of variational parameters to the Gutzwiller-Jastrow factor as well as to the one-body part. Moreover, the projection operator to restore the symmetry of the wave function is introduced. These improvements enable to treat fluctuations with long-ranged as well as short-ranged correlations. A highly generalized wave function is implemented by the Pfaffians introduced by Bouchaud et al., together with the stochastic reconfiguration method introduced by Sorella for the parameter optimization. Our framework offers much higher accuracy for strongly correlated electron systems than the conventional variational Monte Carlo methods.

Effective Hamiltonians for LaFeAsO and LaFePO are derived from the downfolding scheme based on first-principles calculations and provide insights for newly discovered superconductors in the family of LnFeAsO(1-x)F(x), Ln = La, Ce, Pr, Nd, Sm, and Gd. Extended Hubbard Hamiltonians for five maximally localized Wannier orbitals per Fe are constructed dominantly from five-fold degenerate iron-3d bands. They contain parameters for effective Coulomb and exchange interactions screened by the polarization of other electrons away from the Fermi level. The onsite Coulomb interaction estimated as 2.2-3.3eV is compared with the transfer integrals between the nearest-neighbor Fe-3d Wannier orbitals, 0.2-0.3eV, indicating moderately strong electron correlation. The Hund's rule coupling is found to be 0.3-0.6eV. The derived model offers a firm basis for further studies on physics of this family of materials. The effective models for As and P compounds turn Out to have very similar screened interactions with slightly narrower bandwidth for the As compound.

We propose that the proximity of the first-order transition manifested by the quantum tricritical point (QTCP) explains non-Fermi-liquid properties of YbRh2Si2. Here, at the QTCP, a continuous phase transition changes into first order at zero temperature. The non-Fermi-liquid behaviors of YbRh2Si2 are veiled in several prominent mysteries; diverging ferromagnetic susceptibility at the antiferromagnetic transition and enhancement of magnetization as well as specific heat. These puzzles are solved by an unconventional criticality derived from our spin fluctuation theory for the QTCP; especially, diverging ferromagnetic susceptibility is quantitatively reproduced.

We study ground-state properties of the two-dimensional Hubbard model at half filling by improving variational Monte Carlo method and by implementing quantum-number projection and multi-variable optimization. The improved variational wave function enables a highly accurate description of the Mott transition and strong fluctuations in metals. We clarify how anomalous metals appear near the first-order Mott transition. The double occupancy stays nearly constant as a function of the on-site Coulomb interaction in the metallic phase near the Mott transition in agreement with the previous unbiased results. This unconventional metal at half filling is stabilized by a formation of "electron-like pockets" coexisting with an arc structure, which leads to a prominent differentiation of electrons in momentum space. Ail abrupt collapse of' the "pocket" and "arc" drives the first-order Mott transition.

We examine whether the essence and quantitative aspects of electronic excitation spectra are correctly captured by an effective low-energy model constructed from an ab initio downfolding scheme. A global electronic structure is first calculated by ab initio density-functional calculations with the generalized gradient approximation. With the help of constrained density-functional theory, the low-energy effective Hamiltonian for bands near the Fermi level is constructed by the downfolding procedure in the basis of maximally localized Wannier functions. The excited states of this low-energy effective Hamiltonian ascribed to an extended Hubbard model are calculated by using a low-energy solver. As the solver, we employ the Hartree-Fock approximation supplemented by the single-excitation configuration-interaction method considering electron-hole interactions. The present three-stage method is applied to GaAs, where eight bands are retained in the effective model after the downfolding. The resulting spectra well reproduce the experimental results, which indicate that our downfolding scheme offers a satisfactory framework of the electronic-structure calculation, particularly for the excitations and dynamics as well as for the ground state.

We show theoretically that the second layer of He-3 adsorbed on graphite and solidified at 4/7 of the first-layer density is close to the fluid-solid boundary with substantial density fluctuations on the third layer. The solid shows a translational symmetry breaking as in charge-ordered insulators of electronic systems. We construct a minimal model beyond the multiple-exchange Heisenberg model. An unexpectedly large magnetic field required for the measured saturation of magnetization is well explained by the density fluctuations. The emergence of quantum spin liquid is understood from the same mechanism as in the Hubbard model and in K-(ET)(2)CU2(CN)(3) near the Mott transitions.

We reexamine whether the essence of high-T-c superconductivity is contained in doped Hubbard models on the square lattice by using recently developed pre-projected Gaussian-basis Monte Carlo method. The superconducting correlations of the d(x2-y2) wave symmetry in the ground state at distance r decays essentially as r(-3). The upper bound of the correlation at long distances estimated by this unbiased method is 10(-3), indicating that recent extensions of dynamical mean-field theories and variational methods yielded at least an order of magnitude overestimates of it. The correlations are too weak for the realistic account of the cuprate high-T-c superconductivity.

The path-integral renormalization group method is an efficient tool for computing electronic structure of strongly correlated electron systems. Combined with the conventional density functional approaches as a hybrid scheme, it offers a first-principles method for complex materials with involved electron correlation effects. We assess the efficiency and applicability of the hybrid scheme by examining applications to Sr2VO4 and YVO3.

We examine Gaussian-basis Monte Carlo (GBMC) method introduced by Corney and Drummond. This method is based on an expansion of the density-matrix operator (rho) over cap by means of the coherent Gaussian-type operator basis A and does not suffer from the minus sign problem. The original method, however, often fails in reproducing the true ground state and causes systematic errors of calculated physical quantities because the samples are often trapped in some metastable or symmetry broken states. To overcome this difficulty, we combine the quantum-number projection scheme proposed by Assaad, Werner, Corboz, Gull, and Troyer in conjunction with the importance sampling of the original GBMC method. This improvement allows us to carry out the importance sampling in the quantum-number-projected phase-space. Some comparisons with the previous quantum-number projection scheme indicate that, in our method, the convergence with the ground state is accelerated, which makes it possible to extend the applicability and widen the range of tractable parameters in the GBMC method. The present scheme offers an efficient practical way of computation for strongly correlated electron systems beyond the range of system sizes, interaction strengths and lattice structures tractable by other computational methods such as the quantum Monte Carlo method.

We study metal-insulator transitions between Mott insulators and metals. The transition mechanism completely different from the original dynamical mean field theory (DMFT) emerges from a cluster extension of it. A consistent picture suggests that the quasiparticle weight Z remains nonzero through metals and suddenly jumps to zero at the transition, while the gap opens continuously in the insulators. This is in contrast with the original DMFT, where Z continuously vanishes but the gap opens discontinuously. The present results arising from electron differentiation in momentum space agree with recent puzzling bulk-sensitive experiments on CaVO3 and SrVO3.

We clarify that metamagnetic transitions in three dimensions show unusual properties as quantum phase transitions if they are accompanied by changes in Fermi-surface topology. An unconventional universality deeply affected by the topological nature of Lifshitz-type transitions emerges around the marginal quantum critical point (MQCP). Here, the MQCP is defined by the meeting point of the finite temperature critical line and a quantum critical line running on the zero temperature plane. The MQCP offers a marked contrast with the Ising universality and the gas-liquid-type criticality satisfied for conventional metamagnetic transitions. At the MQCP, the inverse magnetic susceptibility chi(-1) has a diverging slope as a function of the magnetization m (namely, \d chi(-1)/dm\ --> infinity) in one side of the transition, which should not occur in any conventional quantum critical phenomena. The exponent of the divergence can be estimated even at finite temperatures. We propose that such an unconventional universality indeed accounts for the metamagnetic transition in ZrZn2.

The Drude weight of the Hubbard model on the two-dimensional square lattice is studied by the exact diaogonalizations applied to clusters up to 20 sites. We carefully examine finite-size effects by consideration of the appropriate shapes of clusters and the appropriate boundary condition beyond the limitation of employing only the simple periodic boundary condition. We successfully capture the behavior of the Drude weight that is proportional to the squared hole doping concentration. Our present result gives a consistent understanding of the transition between the Mott insulator and doped metals. We also find, in the frequency dependence of the optical conductivity, that the mid-gap incoherent part emerges more quickly than the coherent part and rather insensitive to the doping concentration in accordance with the scaling of the Drude weight.

The nature of the quantum valence transition is studied on the basis of the periodic Anderson model with Coulomb repulsion between f and conduction electrons. The density matrix renormalization group calculation for the ground state shows that the first-order valence transition emerges with the quantum critical point with diverging valence susceptibility. Instead of the phase separation in the mean-field result, quantum fluctuations generate a wide region of crossover between the Kondo and mixed valence states. It is found that the superconducting correlation is developed in the Kondo regime near the quantum critical point of the valence transition. The origin is ascribed to the enhanced coherent motion of electrons with valence fluctuation. Remarks on the valence transition are given in connection with Ce compounds and Ce metal. (c) 2006 Elsevier B.V. All rights reserved.

Critical exponents of metal-insulator transitions are studied for an extended Hubbard model within the Hartree-Fock approximation. At zero temperature, we find that the first-order transition line between a symmetry broken (antiferromagnetic or charge-ordered) metal and an insulator terminates at the "marginally quantum critical point'', where an unconventional universality class emerges. This universality is in agreement with the scaling theory and explains the exponents obtained by recent experiments on (V, Cr)(2)O-3 and k-(ET)(2)Cu(Cn)(2)Cl in a unified way as a crossover from the marginally quantum universality and the Ising universality. (c) 2006 Elsevier B.V. All rights reserved.

We study electron correlation effects on quantum criticalities of Lifshitz transitions (LTs), using the mean-field theory based on a preexisting broken symmetry order, in two-dimensional systems. In the presence of interactions, LTs may become discontinuous in contrast to the continuous transition in the original proposal by Lifshitz for noninteracting systems. We find that the quantum criticality at the endpoint of discontinuous LTs, which we call the marginal quantum critical point, belongs to a different universality class from that of the mean-field Ising model. (c) 2006 Elsevier B.V. All rights reserved.

Quantum criticality of metal-insulator transitions in correlated electron systems is shown to belong to an unconventional universality class with violation of the Ginzburg-Landau-Wilson (GLW) scheme formulated for symmetry breaking transitions. This unconventionality arises from an emergent character of the quantum critical point, which appears at the marginal point between the Ising-type symmetry breaking at nonzero temperatures and the topological transition of the Fermi surface at zero temperature. We show that Hartree-Fock approximations of an extended Hubbard model on square lattices are capable of such metal-insulator transitions with unusual criticality under a preexisting symmetry breaking. The obtained universality is consistent with the scaling theory formulated for Mott transitions and with a number of numerical results beyond the mean-field level, implying that preexisting symmetry breaking is not necessarily required for the emergence of this unconventional universality. Examinations of fluctuation effects indicate that the obtained critical exponents remain essentially exact beyond the mean-field level. It further clarifies the whole structure of singularities by a unified treatment of the bandwidth-control and filling-control transitions. Detailed analyses of the criticality, containing diverging carrier density fluctuations around the marginal quantum critical point, are presented from microscopic calculations and reveal the nature as quantum critical "opalescence." The mechanism of emerging marginal quantum critical point is ascribed to a positive feedback and interplay between the preexisting gap formation present even in metals and kinetic energy gain (loss) of the metallic carrier. Analyses of crossovers between GLW type at nonzero temperature and topological type at zero temperature show that the critical exponents observed in (V,Cr)(2)O-3 and kappa-ET-type organic conductors provide us with evidence for the existence of the present marginal quantum criticality.

We study thermodynamic properties of an antiferromagnetic Ising model on the inverse perovskite lattice by using Monte Carlo simulations. The lattice structure is composed of corner-sharing octahedra and contains three-dimensional (3D) geometrical frustration in terms of magnetic interactions. The system with the nearest-neighbor interactions alone does not exhibit any phase transition, leading to a field or by an anisotropy in the interactions. Depending on the anisotropy, they stabilize either a 3D ferrimagnetic state or a partially-disordered antiferromagnetic (PDAF) state with a dimensionality reduction to 2D. By the degeneracy-lifting perturbations, all the transition temperatures of these different ordered states continuously grow form zero, leaving an unusual zero-temperature critical point at the unperturbed point. Such a zero-temperature multicriticality is not observed in other frustrated structures such as face-centered cubic and pyrochlore. The transition to the PDAF state is represented by either the first- or second-order boundaries separated by tricritical lines, whereas the PDAF phase shows 1/3 magnetization plateaus.

We study metal-insulator transitions between Mott insulators and metals. The transition mechanism completely different from the original dynamical mean field theory (DMFT) emerges from a cluster extension of it. A consistent picture suggests that the quasiparticle weight Z remains nonzero through metals and suddenly jumps to zero at the transition, while the gap opens continuously in the insulators. This is in contrast with the original DMFT, where Z continuously vanishes but the gap opens discontinuously. The present results arising from electron differentiation in momentum space agree with recent puzzling bulk-sensitive experiments on CaV O3 and SrV O3. © 2007 The American Physical Society.

We investigate the electronic structure of the transition-metal oxide YVO3 by a hybrid first-principles scheme. The density-functional theory with the local-density-approximation by using the local muffin-tin orbital basis is applied to derive the whole band structure. The electron degrees of freedom far from the Fermi level are eliminated by a downfolding procedure leaving only the V 3d t(2g) Wannier band as the low-energy degrees of freedom, for which a low-energy effective model is constructed. This low-energy effective Hamiltonian is solved exactly by the path-integral renormalization group method. It is shown that the g-round state has the G-type spin and the C-type orbital ordering in agreement with experimental indications. The indirect charge gap is estimated to be around 0.7 eV, which prominently improves the previous estimates by other conventional methods.

We study electron correlation effects on quantum criticalities of Lifshitz transitions at zero temperature, using the mean-field theory based on a preexisting symmetry-broken order, in two-dimensional systems. In the presence of interactions, Lifshitz transitions may become discontinuous in contrast to the continuous transition in the original proposal by Lifshitz for noninteracting systems. We focus on the quantum criticality at the endpoint of discontinuous Lifshitz transitions, which we call the marginal quantum critical point. It shows remarkable criticalities arising from its nature as a topological transition. At the point, for the canonical ensemble, the susceptibility of the order parameter X is found to diverge as In 1/vertical bar delta Delta vertical bar when the "neck" of the Fermi surface collapses at the van Hove singularity. More remarkably, it diverges as vertical bar delta Delta vertical bar(-1) when the electron/hole pocket of the Fermi surface vanishes. Here delta Delta is the amplitude of the mean field measured from the Lifshitz critical point. On the other hand, for the grand canonical ensemble, the discontinuous transitions appear as the electronic phase separation and the endpoint of the phase separation is the marginal quantum critical point. Especially, when a pocket of the Fermi surface vanishes, the uniform charge compressibility kappa diverges as vertical bar delta n vertical bar(-1), instead of chi, where delta n is the electron density measured from the critical point. Accordingly, Lifshitz transition induces large fluctuations represented by diverging chi and/or kappa. Such fluctuations must be involved in physics of competing orders and influence diversity of strong correlation effects.

Combining first-principles calculations with a technique for many-body problems, we investigate the properties of the transition metal oxide Sr2VO4 from the microscopic point of view. By using the local density approximation (LDA), the high-energy band structure is obtained, while screened Coulomb interactions are derived from the constrained LDA and the GW method. The renormalization of the kinetic energy is determined from the GW method. By these downfolding procedures, an effective Hamiltonian at low energies is derived. Applying the path integral renormalization group method to this Hamiltonian, we obtain ground-state properties such as the magnetic and orbital orders. Obtained results are consistent with available experimental data. We find that Sr2VO4 is close to the metal-insulator transition. Furthermore, because of the coexistence and competition of ferromagnetic and antiferromgnetic exchange interactions in this system, an antiferromagnetic and orbital-ordered state with a nontrivial and large unit cell structure is predicted in the ground state. The calculated optical conductivity shows characteristic shoulder structure in agreement with the experimental results. This suggests an orbital selective reduction of the Mott gap.

Divergent carrier-density fluctuations equivalent to the critical opalescence of gas-liquid transition emerge around a metal-insulator critical point at a finite temperature. In contrast to the gas-liquid transitions, however, the critical temperatures can be lowered to zero, which offers a challenging quantum phase transition. We present a microscopic description of such quantum critical phenomena in two dimensions. The conventional scheme of phase transitions by Ginzburg, Landau, and Wilson is violated because of its topological nature. It offers a clear insight into the criticalities of metal-insulator transitions (MIT) associated with Mott or charge-order transitions. Fermi degeneracy involving the diverging density fluctuations generates emergent phenomena near the endpoint of the first-order MIT and must shed new light on remarkable phenomena found in correlated metals such as unconventional cuprate superconductors. It indeed accounts for the otherwise puzzling criticality of the Mott transition recently discovered in an organic conductor. We propose to accurately measure enhanced dielectric fluctuations at small wave numbers.

Filling-control metal-insulator transition on the two-dimensional Hubbard model is investigated by using the cor-relator projection method, which takes into account the momentum dependence of the free energy beyond the dynamical mean-field theory. The phase diagram of metals and Mott insulators is analyzed. Lifshitz transitions occur simultaneously with metal-insulator transitions for large Coulomb repulsion. On the other hand, they are separated each other for smaller Coulomb repulsion, where the phase sandwiched by the Lifshitz and metal-insulator transitions appears to show violation of the Luttinger sum rule. Through the metal-insulator transition, quasiparticles retain nonzero renormalization factor and finite quasi-particle weight on both sides of the transition. This supports that the metal-insulator transition is caused not by the vanishing renormalization factor but by the relative shift of the Fermi level into the Mott gap away from the quasiparticle band, in sharp contrast with the original dynamical mean-field theory. Charge compressibility diverges at the critical end point of the first-order Lifshitz transition at finite temperatures. The origin of the divergence is ascribed to the singular momentum dependence of the quasiparticle dispersion.

Unique features of the nonmagnetic insulator phase are revealed, and the phase diagram of the t-t(') Hubbard model containing the diagonal transfers t(') on a square lattice is presented. Using the path-integral renormalization group method, we find an antiferromagnetic phase for small next-nearest-neighbor transfer t(') and a stripe (or collinear) phase for large t(') in the Mott insulating region of the strong on-site interaction U. For intermediate t(')/t similar to 0.7 at large U/t > 7, we find a longer-period antiferromagnetic-insulator phase with 2x4 structure. In the Mott insulating region, we also find a quantum spin liquid (in other words, a nonmagnetic insulator) phase near the Mott transition to paramagnetic metals for the t-t(') Hubbard model on the square lattice as well as on the anisotropic triangular lattice. Correlated electrons often crystallize to the Mott insulator usually with some magnetic orders, whereas the "quantum spin liquid" has been a long-sought issue. We report numerical evidence that a nonmagnetic insulating phase gets stabilized near the Mott transition with remarkable properties: The two-dimensional Mott insulators on geometrically frustrated lattices contain a phase with gapless spin excitations and degeneracy of the ground state in the whole Brillouin zone of the total momentum. The obtained vanishing spin renormalization factor suggests that spin excitations do not propagate coherently in contrast to conventional phases, where there exist either magnons in symmetry-broken phases or particle-hole excitations in paramagnetic metals. It imposes a constraint on the possible pictures of quantum spin liquids and supports an interpretation for the existence of an unconventional quantum liquid. The present concept is useful in analyzing a variety of experimental results in frustrated magnets including organic BEDT-TTF compounds and He-3 atoms adsorbed on graphite.

Tricritical point in charge-order systems and its criticality are studied for a microscopic model by using the mean-field approximation and exchange Monte Carlo method in the classical limit as well as by using the Hartree-Fock approximation for the quantum model. We study the extended Hubbard model and show that the tricritical point emerges as an endpoint of the first-order transition line between the disordered phase and the charge-ordered phase at finite temperatures. Strong divergences of several fluctuations at zero wavenumber are found and analyzed around the tricritical point. Especially, the charge susceptibility X, and the susceptibility of the next-nearest-neighbor correlation chi(R) are shown to diverge and their critical exponents are derived to be the same as the criticality of the susceptibility of the double occupancy chi(D(O)). The singularity of conductivity at the tricritical point is clarified. We show that the singularity of the conductivity or is governed by that of the carrier density and is given as vertical bar sigma - sigma vertical bar similar to vertical bar g - g(c)vertical bar(Pt)(A log vertical bar g - g(c)vertical bar + B), where g is the effective interaction of the Hubbard model, a. (gc) represents the critical conductivity(interaction) and A and B are constants, respectively. Here, in the canonical ensemble, we obtain p(t) = 2 beta(t) = 1/2 at the tricritical point. We also show that p(t) changes into p(t)' = 2 beta = 1 at the tricritical point in the grand-canonical ensemble when the tricritical point in the canonical ensemble is involved within the phase separation region. The results are compared with available experimental results of organic conductor (DI-DCNQI)(2)Ag.

The nature of the quantum valence transition is studied in the one-dimensional periodic Anderson model with Coulomb repulsion between f and conduction electrons by the density-matrix renormalization group method. It is found that the first-order valence transition emerges with the quantum critical point and the crossover from the Kondo to the mixed-valence states is strongly stabilized by quantum fluctuation and electron correlation. It is found that the superconducting correlation is developed in the Kondo regime near the sharp valence increase. The origin of the superconductivity is ascribed to the development of the coherent motion of electrons with enhanced valence fluctuation, which results in the enhancement of the charge velocity, but not of the charge compressibility. Statements on the valence transition in connection with Ce metal and Ce compounds are given.

Given the successes of the microscopic theory of conventional superconductors, it seems natural to expect a similar all-encompassing theory for high-temperature superconductivity. But is it the best approach? Where are we heading?

Path-integral renormalization-group (PIRG) method is a rapidly developing tool for computing ground state properties of interacting quantum systems on lattices, particularly models for strongly correlated electrons such as the Hubbard model. It has served in clarifying phase diagrams of the Hubbard model containing quantum spin liquid phase. PIRG has also been implemented as a low-energy solver of the effective Hamiltonian for realistic systems. This makes it possible to construct a scheme of first-principles calculation by the hybrid approach combined with the density functional theory.

The Hubbard model with additional intersite interaction 'V' (the extended Hubbard model) is investigated by the correlator projection method (CPM). CPM is a newly developed numerical method that combines the equation-of-motion approach and the dynamical mean-field theory. Using this method, properties of the extended Hubbard Model at quarter filling are discussed with special emphasis on the metal-insulator transition induced by electron-electron correlations. As we increase the interaction, a metal-insulator transition to a charge ordered insulator with antiferromagnetic order occurs at low temperatures, but a metal-insulator transition to a charge ordered insulator without magnetic symmetry breaking occurs at intermediate temperatures. Here, the magnetic order is found to be confined to low temperatures because of the smallness of the exchange coupling J(eff). The present results are in sharp contrast to the Hatree-Fock approximation whereas they are in agreement with the experimental results on quarter-filled materials with strong correlations Such as organic BEDT-TTF conductors.

A new scheme of first-principles computation for strongly correlated electron systems is proposed. This scheme starts from the local-density approximation (LDA) at high-energy band structure, while the low-energy effective Hamiltonian is constructed by a downfolding procedure using combinations of the constrained-LDA and the GW method. The obtained low-energy Hamiltonian is solved by the path-integral renormalization-group method, where spatial and dynamical fluctuations are fully considered. An application to Sr2VO4 shows that the scheme is powerful in agreement with experimental results. It further predicts a nontrivial orbital-stripe order.

We study three regimes of the Mott transitions characterized by classical, marginally quantum, and quantum. In the classical regime, the quantum degeneracy temperature is lower than the critical temperature of the Mott transition Tc, below which the first-order transition occurs. The quantum regime describes the Tc =0 boundary of the continuous transition. The marginal quantum region appears sandwiched by these two regimes. The classical transition is described by the Ising universality class. However, the Ginzburg-Landau-Wilson scheme breaks down when the quantum effects dominate. The marginal quantum critical region is categorized to an unusual universality class, where the order parameter exponent β, the susceptibility exponent γ, and the field exponent δ are given by β=d/2, γ=2-d/2, and δ=4/d, respectively, with d being the spatial dimensionality. It is shown that the transition is always at the upper critical dimension irrespective of the spatial dimensions. Therefore the mean-field exponents and the hyperscaling description become both valid at any dimension. The obtained universality classes agree with the recent experimental results on the Mott criticality in organic conductors such as κ- (ET)2 Cu [N (CN)2] Cl and transition-metal compounds such as V2 O3. The marginal quantum criticality is characterized by the critically enhanced electron-density fluctuations at small wave number. The characteristic energy scale of the density fluctuation extends to the order of the Mott gap in contrast to the spin and orbital fluctuation scales and causes various unusual properties. The mode coupling theory shows that the marginal quantum criticality further generates non-Fermi-liquid properties in the metallic side. The effects of the long-range Coulomb force in the filling-control Mott transition are also discussed. A mechanism of high-temperature superconductivity emerges from the density fluctuations at small wave number inherent in the marginal quantum criticality of the Mott transition. The mode coupling theory combined with the Eliashberg equation predicts the superconductivity of the d x2 - y2 symmetry with the transition temperature of the correct order of magnitude for the realistic parameters for the cuprate superconductors. Experimental results on the electron differentiations established in the angle-resolved photoemission experiments are favorably compared with the present prediction. The tendency for the spatial inhomogeneity is a natural consequence of this criticality. © 2005 The American Physical Society.

We study three regimes of the Mott transitions characterized by classical, marginally quantum, and quantum. In the classical regime, the quantum degeneracy temperature is lower than the critical temperature of the Mott transition T-c, below which the first-order transition occurs. The quantum regime describes the T-c=0 boundary of the continuous transition. The marginal quantum region appears sandwiched by these two regimes. The classical transition is described by the Ising universality class. However, the Ginzburg-Landau-Wilson scheme breaks down when the quantum effects dominate. The marginal quantum critical region is categorized to an unusual universality class, where the order parameter exponent beta, the susceptibility exponent gamma, and the field exponent delta are given by beta=d/2, gamma=2-d/2, and delta=4/d, respectively, with d being the spatial dimensionality. It is shown that the transition is always at the upper critical dimension irrespective of the spatial dimensions. Therefore the mean-field exponents and the hyperscaling description become both valid at any dimension. The obtained universality classes agree with the recent experimental results on the Mott criticality in organic conductors such as kappa-(ET)(2)Cu[N(CN)(2)]Cl and transition-metal compounds such as V2O3. The marginal quantum criticality is characterized by the critically enhanced electron-density fluctuations at small wave number. The characteristic energy scale of the density fluctuation extends to the order of the Mott gap in contrast to the spin and orbital fluctuation scales and causes various unusual properties. The mode coupling theory shows that the marginal quantum criticality further generates non-Fermi-liquid properties in the metallic side. The effects of the long-range Coulomb force in the filling-control Mott transition are also discussed. A mechanism of high-temperature superconductivity emerges from the density fluctuations at small wave number inherent in the marginal quantum criticality of the Mott transition. The mode coupling theory combined with the Eliashberg equation predicts the superconductivity of the d(x)(2)-y(2) symmetry with the transition temperature of the correct order of magnitude for the realistic parameters for the cuprate superconductors. Experimental results on the electron differentiations established in the angle-resolved photoemission experiments are favorably compared with the present prediction. The tendency for the spatial inhomogeneity is a natural consequence of this criticality.

We present a quantum-number projection technique and its implementation to the recently proposed path-integral renormalization group (PIRG) method, which has been quite a powerful tool in investigating strongly correlated electron systems. By this extension, the PIRG can handle excited states with different quantum numbers in addition to the ground state and precision of solution is highly improved. By taking Hubbard models as an example, we demonstrate its feasibility. (c) 2005 Elsevier B.V. All rights reserved.

Metal-insulator transition is one of hot issues in condensed-matter physics. The transition between the doped metal and the Mott insulator can be realized in the Hubbard model theoretically. It was recently found that the ground state of the one-dimensional Hubbard model with next-nearest-neighbor hopping clearly shows partial ferromagnetism in the metallic phase near the half-filled Mott insulator. We study the hole density (delta) dependence of the charge susceptibility (chi(c)) of this model by means of exact diagonalization of finite-size clusters. The behavior of the charge susceptibility characterizes the nature of the metal-insulator transition. We find that a region where the critical exponent alpha defined by chi(c) proportional to delta(-alpha) is alpha = 3 in sharp contrast with the known exponent alpha = 1 in the ordinary one-dimensional Hubbard model. (c) 2005 Elsevier B.V. All rights reserved.

The gas-liquid transition is a first-order transition terminating at a finite-temperature critical point with diverging density fluctuations. The Mott transition, a metal-insulator transition driven by Coulomb repulsion between electrons, has been identified with this textbook transition. However, the critical temperature of the Mott transition can be suppressed, leading to unusual quantum criticality, which results in a breakdown of the conventional Ginzburg-Landau-Wilson scheme. This accounts for non-Fermi-liquid-like properties, and strongly momentum-dependent quasiparticles as in many materials near the Mott insulator. Above all, the mode-coupling theory of the density fluctuations supports d-wave superconductivity at the order of 100 K for the relevant parameters of copper oxide superconductors.

We discuss different methods of calculation of the screened Coulomb interaction U in transition metals and compare the so-called constraint local-density approximation (LDA) with the GW approach. We clarify that they offer complementary methods of treating the screening and therefore should serve for different purposes. The analysis is illustrated by calculations for the ferromagnetic Ni. In the ab initio GW method, the renormalization of bare on-site Coulomb interactions between 3d electrons (being of the order of 20-30 eV) occurs mainly through the screening by the same 3d electrons, treated in the random-phase approximation (RPA). The basic difference of the constraint-LDA method from the GW method is that it deals with the neutral processes, where the Coulomb interactions are additionally screened by the "excited" electron, since it continues to stay in the system. This is the main channel of screening by the itinerant (4sp) electrons, which is especially strong in the case of transition metals and missing in the GW approach, although the details of this screening may be affected by additional approximations, which typically supplement these two methods. The major drawback of the conventional constraint-LDA method is that it does not allow us to treat the energy dependence of U, while the full GW calculations require heavy computations. We propose a promising approximation based on the combination of these two methods. First, we take into account the screening of Coulomb interactions in the 3d-electron-like bands located near the Fermi level by the states from the orthogonal subspace, using the constraint-LDA methods. The obtained interactions are further renormalized within the bands near the Fermi level in RPA. This allows the energy-dependent screening by electrons located near the Fermi level, including the same 3d electrons.

We discuss different methods of calculation of the screened Coulomb interaction U in transition metals and compare the so-called constraint local-density approximation (LDA) with the GW approach. We clarify that they offer complementary methods of treating the screening and therefore should serve for different purposes. The analysis is illustrated by calculations for the ferromagnetic Ni. In the ab initio GW method, the renormalization of bare on-site Coulomb interactions between 3d electrons (being of the order of 20-30 eV) occurs mainly through the screening by the same 3d electrons, treated in the random-phase approximation (RPA). The basic difference of the constraint-LDA method from the GW method is that it deals with the neutral processes, where the Coulomb interactions are additionally screened by the "excited" electron, since it continues to stay in the system. This is the main channel of screening by the itinerant (4sp) electrons, which is especially strong in the case of transition metals and missing in the GW approach, although the details of this screening may be affected by additional approximations, which typically supplement these two methods. The major drawback of the conventional constraint-LDA method is that it does not allow us to treat the energy dependence of U, while the full GW calculations require heavy computations. We propose a promising approximation based on the combination of these two methods. First, we take into account the screening of Coulomb interactions in the 3d-electron-like bands located near the Fermi level by the states from the orthogonal subspace, using the constraint-LDA methods. The obtained interactions are further renormalized within the bands near the Fermi level in RPA. This allows the energy-dependent screening by electrons located near the Fermi level, including the same 3d electrons. ©2005 The American Physical Society.

Several useful thermodynamic relations are derived for metal-insulator transitions, as generalizations of the Clausius-Clapeyron and Eherenfest theorems. These relations hold in any spatial dimensions and at any temperatures. First, they relate several thermodynamic quantities to the slope of the metal-insulator phase boundary drawn in the plane of the chemical potential and the Coulomb interaction in the phase diagram of the Hubbard model. The relations impose constraints on the critical properties of the Mott transition. These thermodynamic relations are indeed confirmed to be satisfied in the cases of the one- and two-dimensional Hubbard models. One of these relations yields that at the continuous Mott transition with a diverging charge compressibility, the doublon susceptibility also diverges. The constraints on the shapes of the phase boundary containing a first-order metal-insulator transition at finite temperatures are clarified based on the thermodynamic relations. For example, the first-order phase boundary is parallel to the temperature axis asymptotically in the zero temperature limit. The applicability of the thermodynamic relations are not restricted only to the metal-insulator transition of the Hubbard model, but also hold in correlated systems with any types of phases in general. We demonstrate such examples in an extended Hubbard model with intersite Coulomb repulsion containing the charge order phase.

Titanate compounds have been recognized as key materials for understanding the coupling of magnetism and orbitals in strongly correlated electron systems. In the perovskite Ti oxide RTiO3 (where R represents the trivalent rare-earth ions), which is a typical Mott-Hubbard insulator, the Ti t(2g) orbitals and spins in the 3d(1) state couple each other through the strong electron correlations, resulting in a rich variety of orbital-spin phases. One way of controlling the coupling is to change the tiltings of the TiO6 octahedra (namely the GdFeO3-type distortion) by varying the R ions, through which the relative ratio of the electron bandwidth to the Coulomb interaction is controlled. With this control, these Mott insulators exhibit an antiferromagnetic-to-ferromagnetic (AFM-FM) phase transition, which has turned out to be a consequence of rich orbital physics in these materials. The origin and nature of orbital-spin structures of these Mott insulators have been intensively studied both experimentally and theoretically. When the Mott insulators are doped with carriers, the titanates show touchstone properties of the filling controlled Mott transition. In this paper, we first review the state of the art on the studies for understanding physics contained in the properties of the perovskite titanates. On the properties of the insulators, we focus on the following three topics: (1) the origin and nature of the ferromagnetism as well as the orbital ordering in the compounds with relatively small R ions such as GdTiO3 and YTiO3, (2) the origin of the G-type antiferromagnetism and the orbital state in LaTiO3 and (3) the orbital-spin structures in other AFM(G) compounds with relatively large R ions (R = Ce, Pr, Nd and Sm). On the basis of these discussions, we discuss the whole phase diagram together with mechanisms of the magnetic phase transition. On the basis of the microscopic understanding of the orbital-spin states, we show that the Ti t(2g) degeneracy is inherently lifted in the titanates, which allows the single-band descriptions of the ground-state and the low-energy electronic structures as a good starting point. Our analyses indicate that these compounds offer good touchstone materials described by the single-band Hubbard model on the cubic lattice. From this insight, we also re-analyse the hole-doped titanates R(1-x)A(x)TiO(3) (where A represents the divalent alkaline-earth ions). Experimentally revealed filling- and bandwidth-dependent properties and the critical behaviour of the metal-insulator transitions are discussed in the light of theories based on the single-band Hubbard models.

We propose a systematic procedure for constructing effective models of strongly correlated materials. The parameters, in particular the on-site screened Coulomb interaction U, are calculated from first principles, using the random-phase approximation. We derive an expression for the frequency-dependent U(omega) and show, for the case of nickel, that its high-frequency part has significant influence on the spectral functions. We propose a scheme for taking into account the energy dependence of U(omega), so that a model with an energy-independent local interaction can still be used for low-energy properties.

Phenomenological theory of the Mott transition is presented. When the critical temperature of the Mott transition is much higher than the quantum degeneracy temperature, the transition is essentially described by the Ising universality class. Below the critical temperature, phase separation or first-order transition occurs. However, if the critical point is involved in the Fermi degeneracy region, a quantum critical point appears at zero temperature. The originally single Mott critical point generates subsequent many unstable fixed points through various Fermi surface instabilities induced by the Mott criticality characterized by the diverging charge susceptibility or doublon susceptibility. This occurs in marginal quantum-critical region. Charge, magnetic and superconducting instabilitites compete severely under these critical charge fluctuations. The quantum Mott transition triggers multi-furcating criticality, which goes beyond the conventional concept of multicriticality in quantum phase transitions. Near the quantum Mott transition, the criticality generically drives growth of inhomogeneous structure in the momentum space with singular points of flat dispersion on the Fermi surface. The singular points determine the quantum dynamics of the Mott transition by the dynamical exponent z = 4. We argue that many of filling-control Mott transitions are classified to this category. Recent numerical results as well as experimental results on strongly correlated systems including transition metal oxides, organic materials and He-3 layer adsorbed on a substrate are consistently analyzed especially in two-dimensional systems. The mechanism of cuprate high-T-c superconductivity is also discussed in the light of the present insight and interpreted from the multi-furcation instability.

The origin of the antiferromagnetic order and puzzling properties of LaTiO3 as well as the magnetic phase diagram of the perovskite titanates are studied theoretically. We show that in LaTiO3, the t(2g) degeneracy is eventually lifted by the La cations in the GdFeO3-type structure, which generates a crystal field. This allows the description of the low-energy structure of LaTiO3 by a single-band Hubbard model as a good starting point. The lowest-orbital occupation in this crystal field stabilizes the AFM(G) state, and well explains the spin-wave spectrum of LaTiO3 obtained by the neutron scattering experiment. The orbital-spin structures for RTiO3 where R = Pr, Nd and Sm are also accounted for by the same mechanism. We point out that through generating the R crystal field, the GdFeO3-type distortion has a universal relevance in determining the orbital-spin structure of the perovskite compounds in competition with the Jahn-Teller mechanism, which has been overlooked in the literature. Since the GdFeO3-type distortion is a universal phenomenon as is seen in a large number of perovskite compounds, this mechanism may also play important roles in other compounds of this type.

A new numerical algorithm for interacting fermion systems to treat the grand-canonical ensemble is proposed and examined by extending the path-integral renormalization group method. To treat the grand-canonical ensemble, the particle-hole transformation is applied to the Hamiltonian and basis states. In the interaction-term projection, the Stratonovich-Hubbard transformation which hybridizes up and down spin electrons is introduced. By using this method, the phase diagram of the two-dimensional Hubbard model with next-nearest-neighbor transfer is accurately determined by treating the filling-control (FC) and bandwidth-control (BC) Mott transitions on the same ground. A V-shaped Mott insulating phase is obtained in the plane of the chemical potential and the Coulomb interaction, where the transitions at the corner (BC) and the edges (FC) show contrasted characters with large critical fluctuations near the edges coexisting with the first-order transition at the corner. This contrasted behavior is shown to be consistent with the V-shape structure of the phase boundary because of a general relation, in which the slope of the metal-insulator transition line in the phase diagram is expressed by thermodynamic quantities. The V-shaped opening of the Mott gap is favorably compared with the experimental results of the transition metal oxides.

Mott transitions are studied in the two-dimensional Hubbard model by a non-perturbative theory of correlator projection that systematically includes spatial correlations into the dynamical mean-field theory. A nonzero second-neighbor transfer yields a first-order Mott transition at finite temperatures ending at a critical point. (C) 2004 Elsevier B.V. All rights reserved.

We achieved room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser by current injection. This is the first time ever that room temperature continuous wave operation of a photonic crystal diode laser has been realized. This laser features single mode oscillation over a large area, which is impossible for conventional lasers. In this work, we optimized the epitaxial layer composition for better carrier confinement and clarified the relationship between the diameter of the air holes in the photonic crystal and the threshold current of the laser in order to estimate the optimized threshold current. (C) 2004 Optical Society of America.

We present a quantum-number projection technique which enables us to exactly treat spin, momentum, and other symmetries embedded in the Hubbard model. By combining this projection technique, we extend the path-integral renormalization-group method to improve the efficiency of numerical computations. By taking numerical calculations for the standard Hubbard model and the Hubbard model with next-nearest-neighbor transfer, we show that the present extended method can extremely enhance numerical accuracy and that it can handle excited states, in addition to the ground state.

We propose a systematic procedure for constructing effective models of strongly correlated materials. The parameters, in particular the on-site screened Coulomb interaction U, are calculated from first principles, using the random-phase approximation. We derive an expression for the frequency-dependent U(ω) and show, for the case of nickel, that its high-frequency part has significant influence on the spectral functions. We propose a scheme for taking into account the energy dependence of U(ω), so that a model with an energy-independent local interaction can still be used for low-energy properties.

The origin of the G-type antiferromagnetism [AFM(G)] and puzzling properties of RTiO3 with R=La are studied. We clarify that the crystal field from La caused by the GdFeO3-type distortion lifts the t(2g) degeneracy at Ti 3d orbitals. The lift stabilizes the AFM(G) with spin-exchange constant in agreement with neutron-scattering results. The orbital-spin structures for R=Pr, Nd, and Sm are also consistent with experiments. We propose that the GdFeO3-type distortion has a universal mechanism of controlling orbital-spin structure competing with the Jahn-Teller (JT) mechanism.

The two-dimensional half-filled Hubbard model is studied by a nonperturbative analytic theory of correlator projection. The dynamical mean-field approximation (DMFA) is reproduced at the first-order projection and then improved by systematic inclusion of spatial correlations at higher orders. A geometrical frustration induces a first-order Mott transition surface with a finite-temperature critical end curve and related crossovers. Growth of antiferromagnetic correlations gives single-particle spectra strongly modified from DMFA with shadow bands and flat dispersions observed in high-T-c cuprates.

A second-order extrapolation method is presented for shell model calculations, where shell model energies of truncated spaces are well described as a function of energy variance by quadratic curves, and exact shell model energies can be obtained by the extrapolation. This new extrapolation can give more precise energy than those of first-order extrapolation method. It is also clarified that first-order extrapolation gives a lower limit of shell model energy. In addition to the energy, we derive the second-order extrapolation formula for expectation values of other observables.

We review recent studies on developing tools for quantum complex phenomena. The tools have been applied for clarifying the perspective of the Mott transitions and the phase diagram of metals, Mott insulators and magnetically ordered phases in the two-dimensional Hubbard model. The path-integral renormalization-group (PIRG) method has made it possible to numerically study correlated electrons even with geometrical frustration effects without biases. It has numerically clarified the phase diagram at zero temperature, T = 0, in the parameter space of the onsite Coulomb repulsion, the geometrical frustration amplitude and the chemical potential. When the bandwidth is controlled at half filling, the first-order transition between insulating and metallic phases is evidenced. In contrast, the filling-control transition shows diverging critical fluctuations for spin and charge responses with decreasing doping concentration. Near the Mott transition, a nonmagnetic spin-liquid phase appears in a region with large frustration effects. The phase is characterized remarkably by gapless spin excitations and the vanishing dispersion of spin excitations. Magnetic orders quantum mechanically melt through diverging magnon mass. The correlator projection method (CPM) is formulated as an extension of the operator projection theory. This method also allows an extension of the dynamical mean-field theory (DMFT) with systematic inclusion of the momentum dependence in the self-energy. It has enabled determining the phase diagram at T > 0, where the boundary surface of the first-order metal-insulator transition at half filling terminates on the critical end curve at T = T,. The critical end curve is characterized by the diverging compressibility. The single particle spectra show strong renormalization of low-energy spectra, generating largely momentum dependent and flat dispersion. The results of two tools consistently suggest that the strong competitions of various phases with underlying diverging compressibility can induce an emergence near a new type of quantum criticality distinguished from the conventional and simple quantum. critical phenomena.

Path-integral renormalization group (PIRG) method has been developed for studying strongly correlated electron systems. In a wide range of systems including Hubbard-type models, this method overcomes a number of difficulties known in the Monte-Carlo-type methods such as the negative sign problem. This method has been combined with a procedure of quantum number projection and grand canonical ensemble method as well, which contribute to a wider applicability. The quantum-number projected PIRG enables calculations of excited spectra with a specified momentum or spin. We review recent numerical results on strongly correlated electron systems studied by this method. By using the methods, we determine the phase diagram of the two-dimensional Hubbard model in the parameter space of the onsite interaction U, strength of the geometrical frustration effects defined by the ratio between next-nearest to nearest neighbor transfer integrals, t'/t, and the chemical potential. It reveals severe competitions of various phases. The phase diagram contains a remarkable nonmagnetic Mott insulator phase with gapless and dispersionless spin excitations, sandwitched by the first-order Mott transition and the antiferromagnetic transition. The first-order character becomes more continuous one with increasing the frustration effect.

The origin of the G-type antiferromagnetism [AFM(G)] and puzzling properties of [Formula presented] with [Formula presented] are studied. We clarify that the crystal field from La caused by the [Formula presented]-type distortion lifts the [Formula presented] degeneracy at Ti [Formula presented] orbitals. The lift stabilizes the AFM(G) with spin-exchange constant in agreement with neutron-scattering results. The orbital-spin structures for [Formula presented], Nd, and Sm are also consistent with experiments. We propose that the [Formula presented]-type distortion has a universal mechanism of controlling orbital-spin structure competing with the Jahn-Teller (JT) mechanism. © 2003 The American Physical Society.

Metals approaching the Mott insulator generate a new hierarchy in the electronic structure accompanied by an electron differentiation with emergence of strongly momentum dependent structure, beyond the Mott-Hubbard, Brinkman-Rice and Slater pictures of the Mott transition. To consider such nonlinear phenomenon, we develop an analytic nonperturbative theory based on operator projections combined with a self-consistent treatment of the low-energy excitations. This reproduces the Hubbard bands, Mott gap, spin fluctuations, mass divergence, diverging charge compressibility, and strongly renormalized flat and damped dispersion similar to angle-resolved photoemission data in high-T(c) cuprates. Electronic spectra show a remarkable similarity to numerical results. (C) 2002 Elsevier Science Ltd. All rights reserved.

The relationship among the Wigner crystal, charge ordering, and the Mott insulator is studied by the path-integral renormalization group method in two-dimensional systems with long-range Coulomb interaction. In contrast to the insensitivity of the Hartree-Fock results, the stability of the solid drastically decreases with the decrease in the lattice commensurability. The transition to liquid occurs at the electron gas parameter r(s) similar to 2 for the filling n = 1/2, showing a large reduction from r(s) similar to 35 in the continuum limit. A correct account of quantum fluctuations is crucial to understanding the charge-order stability generally observed only at simple fractional fillings and the nature of quantum liquids away from them.

We study phase diagrams of the Hubbard model on anisotropic triangular lattices, which also represents a model for kappa-type BEDT-TTF compounds. In contrast with mean-field predictions, path-integral renormalization group calculations show a universal presence of a nonmagnetic insulator sandwiched by an antiferromagnetic insulator and paramagnetic metals. The nonmagnetic phase does not show simple translational symmetry breakings such as flux phases, implying a genuine Mott insulator. We discuss possible relevance to the nonmagnetic insulating phase found in kappa-(ET)(2)Cu-2(CN)(3).

We present an algorithm to systematically improve wavefunctions in the variational Monte Carlo method for the t-J model. The ground-state wavefunction is approximated by a linear combination of single-particle states with Gutzwiller projection. The single-particle states are successively generated according to the numerical path-integral renormalization group (PIRG) procedure. In the initial step, the present method reduces to the usual variational Monte Carlo method. As the number of single-particle states increases, the wavefunction converges to the ground-state wavefunction. Applying this method to the two-dimensional t-J model, we have confirmed that the wavefunction, which is composed of a small number of single-particle states, gives a good estimate of the ground-state energy. This algorithm does not suffer from the negative sign problem and can be applied to the models with strong correlations. (C) 2002 Published by Elsevier Science Ltd.

We propose a new shell model method, combining the Lanczos diagonalization and extrapolation methods. This method can give accurate shell model energy from a series of shell model calculations with various truncation spaces, in a well-controlled manner. Its feasibility is demonstrated by taking fp shell calculations.

The ground-state phase diagram is numerically studied for an electronic model consisting of the spin exchange term (J) and the correlated hopping term (t3: the three-site term). This model has no single-particle hopping and the ratio of the two terms is controlled by a parameter α≡4t3/J. The case of α=1 corresponds to complete suppression of single-particle hopping in the strong-coupling limit of the Hubbard model. In one dimension, phase separation takes place below a critical value αc = 0.36-0.63 which depends on the electron density. Spin gap opens in the whole region except the phase-separated one. For α ≳ 1.2 and low hole densities, charge-density-wave correlations are the most dominant, whereas singlet-pairing correlations are the most dominant in the remaining region. The possibility of superconductivity in the two-dimensional case is also discussed, based on equal-time pairing correlations. © 2002 Elsevier Science Ltd. All rights reserved.

Thermodynamic and dynamical properties of filling-control metal-insulator transition (MIT) in the Hubbard model are studied by the operator projection method, especially in two dimensions. This is a non-perturbative analytic approach to many-body systems. The present theory incorporates the Mott-Hubbard, Brinkman-Rice and Slater pictures of the MIT into a unified framework, together with reproducing low-energy narrow band arising from spin-charge fluctuations. At half filling, single-particle spectra A(omega, k) show formation of two Hubbard bands and their antiferromagnetic shadows separated by a Mott gap in the plane of energy omega and momentum k with lowering temperatures. These four bands produce splitting to two low-energy narrow bands and two SDW-like bands in the dispersion. Near half filling, the low-energy narrow band persists at low temperatures. This narrow band has a particularly weak dispersion and large weights around (pi, 0) and (0, pi) momenta. The velocity of these low-energy excitations is shown to vanish towards the MIT, indicating the mass divergence as in the Brinkman-Rice picture, but most prominently around (pi, 0) and (0, pi) with strong momentum dependence. This reflects the suppression of the coherence near the MIT. Main structures in A(w, k) show remarkable similarities to quantum Monte-Carlo results in two dimensions as well as in the one-dimensional Hubbard model. The charge compressibility appears to diverge with decreasing doping concentration in both one and two dimensions in agreement with the exact and quantum Monte-Carlo results. We also discuss implications of the flat dispersion formed near the Fermi level to the observations in high-T-c cuprate superconductors.

The possibility of the D-3d distortion of TiO6 octahedra is examined theoretically in order to understand the origin of the G-type antiferromagnetism [AFM(G)] and experiment ally observed puzzling properties of LaTiO3. By utilizing an effective spin and pseudospin Hamiltonian with the strong Coulomb repulsion, it is shown that the AFM(G) state is stabilized through the lift of the t(2g)-orbital degeneracy accompanied by a tiny D-3d-distortion. The estimated spin-exchange interaction is in agreement with that obtained by the neutron-scattering experiment. Moreover, the level-splitting energy due to the distortion can be considerably larger than the, spin-orbit interaction even when the distortion becomes smaller than the detectable limit under the available experimental resolution. This suggests that the orbital momentum is fully quenched and the relativistic spin-orbit interaction is not effective in this system, in agreement with the result of a recent neutron-scattering experiment.

Numerical studies on Mott transitions caused by the control of the ratio between bandwidth and electron-electron interaction (U) are reported. By using the recently proposed path-integral renormalization group (PIRG) algorithm, physical properties near the transitions, in the ground state of two-dimensional half-filled models with the nearest and the next-nearest neighbor transfers (-t and t', respectively) are studied as a prototype of geometrically frustrated system. The nature of the bandwidth-control transitions shows sharp contrast with that of the filling-control transitions: First, the metal-insulator and magnetic transitions axe separated each other and the metal-insulator (MI) transition occurs at smaller U, although the both transition interactions U increase vith increasing t'. Both transitions do not contradict the first-order transitions for smaller t'/t while the MI transitions become continuous type accompanied by emergence of unusual metallic phase near the transition for large t'/t. A nonmagnetic insulator phase is stabilized between MI and AF transitions. The region of the nonmagnetic insulator becomes wider with increasing t'/t. The phase diagram naturally connects two qualitatively different limits, namely the Hartree Fock results at small t'/t and speculations in the strong coupling Heisenberg limit.

A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two procedures lead to a better approximation, The first is a numerical renormalization, which optimizes the chosen basis and projects onto the ground state within the fixed dimension, L, of the Hilbert space. The second is an increase of the dimension of the truncated Hilbert space, which enables the linear combination to converge to a better approximation. The extrapolation L --> infinity after the convergence removes the approximation error systematically. This algorithm does not suffer from the negative sign problem and can be applied to systems in any spatial dimension and arbitrary lattice structure. The efficiency is tested and the implementation explained for two-dimensional Hubbard models where Slater determinants are employed as chosen basis. Our results with less than 400 chosen basis indicate good accuracy within the errorbar of the best available results as those of the quantum Monte Carlo for energy and other physical quantities.

The properties and mechanism of the magnetic phase transition of the perovskite-type Ti oxides, which is driven by the Ti-O-Ti bond angle distortion, are studied theoretically by using the effective spin and pseudospin Hamiltonian with strong Coulomb repulsion. It is shown that the A-type antiferromagnetic (AFM(A)) to ferromagnetic (FM) phase transition occurs as the Ti-O-Ti bond angle is decreased. Through this phase transition, the orbital state changes only little whereas the spin-exchange coupling along the c-axis is expected to change from positive to negative nearly continuously and approaches aero at the phase boundary. The resultant strong two-dimensionality in the spin coupling causes rapid suppression of the critical temperature, as observed experimentally. It may induce large quantum fluctuations in this region.

Superconducting mechanism mediated by interband exchange Coulomb repulsion is examined in an extended two-band Hubbard models with a wide band crossing the Fermi level and coexisting with a narrower band located at moderately lower energy. We apply newly developed path-integral renormalization group method to reliably calculate pairing correlations. The correlation shows marked enhancement at moderate amplitudes of the exchange Coulomb repulsion taken smaller than the on-site repulsion for the narrower band. The pairing symmetry is s-wave while it has unconventional phases with the opposite sign between the order parameters on the two bands, in agreement with the mean-field prediction. Since the band structure of recently discovered superconductor MgB2 shares basic similarities with our model, we propose that the present results provide a relevant clue for the understanding of the superconducting mechanism in MgB2 as well as in this class of multi-band materials with good metallic conduction in the normal state.

Dissipation effects on a single Josephson junction are studied based on a harmonic-oscillator model in the weak coupling region. It is shown that the system is controlled by two characteristic energy scales. The origin of these energy scales is explained in terms of a classical plasma problem. This feature provides a new viewpoint on the superconductor-insulator transition of small Josephson junctions. (C) 2001 Elsevier Science B.V. All rights reserved.

A new non-perturbative framework for many-body correlated systems is formulated by extending the operator projection method (OPM). This method offers a systematic expansion which enables us to project into the low-energy structure after extracting the higher-energy hierarchy. This method also opens a way to systematically take into account the effects of collective excitations. The Mott-Hubbard metal-insulator transition in the Hubbard model is studied by means of this projection beyond the second order by taking into account magnetic and charge fluctuations in the presence of the high-energy Mott-Hubbard structure. At half filling, the Mott-Hubbard gap is correctly reproduced between the separated two bands. Near half filling, strongly renormalized low-energy single-particle excitations coexisting with the Mott-Hubbard bands are shown to appear. The significance of the momentum-dependent self-energy in the results is stressed.

Different models for doping of two-orbital chains with mobile S = 1/2 fermions and strong, ferromagnetic (FM) Hund's rule couplings stabilizing the S = I spins are investigated by density matrix renormalization group (DMRG) methods. The competition between antiferromagnet;ic (AF) and FM order leads to a rich phase digram with a narrow FM region for weak AF couplings and strongly enhanced triplet pairing correlations. Without a level difference between the orbitals, the spin gap persists upon doping, whereas gapless spin excitations are generated by interactions among itinerant polarons in the presence of a level difference. In the charge sector we find dominant singlet pairing correlations without a level difference, whereas upon the inclusion of a Coulomb repulsion between the orbitals or with it level difference, charge density wave (CDW) correlations decay slowest. The string correlation functions remain finite upon doping for all models.

Aspects of electron critical differentiation are clarified in the proximity of the Mott insulator. The flattening of the quasiparticle dispersion appears around momenta (pi ,0) and (0,pi) On Square lattices and determines the criticality of the metal-insulator transition with the suppressed coherence in that momentum region of quasiparticles. Such coherence suppression at the same time causes an instability to the superconducting state if a proper incoherent process is retained. The d-wave pairing interaction is generated from such retained processes without disturbance from the coherent single-particle excitations. Pseudogap phenomena widely observed in the underdoped cuprates are then naturally understood from the mode-mode coupling of d-wave superconducting (dSC) fluctuations with antiferromagnetic (AFM) ones. When we assume the existence of a strong d-wave pairing force repulsively competing with AFM fluctuations under the formation of flat and damped single-particle dispersion, we reproduce basic properties of the pseudogap seen in the magnetic resonance, neutron scattering, angle resolved photoemission and tunneling measurements in the cuprates. (C) 2000 Elsevier Science Ltd. All rights reserved.

Magnetic properties of underdoped high-T-c cuprates characterized by a spin gap are interpreted in a unified scheme based on the mode-mode coupling theory. By taking one phenomenological relation for the damping rate of the collective modes, it takes account of two different types of pseudogap behavior in spin excitations and spin gap: (I) the damping rate of spin excitations decreases as the temperature decreases, but the spin correlation length does not; (II) the spin correlation length itself turns to decrease. In case (I), low-energy spectral weights shift to higher energies near the spin gap determined by the super conducting transition temperature, which reproduces the observed resonance peak. (C) 2000 Elsevier Science Ltd. All rights reserved.

We numerically demonstrate that the spin-gap and the pairing correlation are enhanced, if the band structure is adjusted to become Rat at the Fermi level near half-filling in strongly correlated electron systems. We show indications that the incoherent charge transport may give rise to the superconducting instability in doped Mott insulators. Based on the numerical results. we discuss the possibility of flat-band induced superconductivity. (C) 2000 Elsevier Science Ltd. All rights reserved.

Diffuse panbronchiolitis (DPB) is a pulmonary disease of unknown origin with inflammation in the respiratory bronchioles, bronchiectasis, and recurrent sinusitis. Patients with DPB suffer from chronic airway infections resulting from mucociliary dysfunction. Whereas a high concentration of nasal nitric oxide (NO) has been documented in healthy subjects, only two diseases are known to reduce nasal NO: primary ciliary dyskinesia syndrome and cystic fibrosis. We hypothesized that patients with DPB have abnormal revels of nasal NO. To test our hypothesis, we measured NO with the chemiluminescence technique. Air was sampled directly from the nose in 15 healthy subjects and eight patients with DPB. Nasal NO was 88% tower in DPB patients than in the age-matched control subjects (69 +/- 70 versus 556 +/- 87 nl/min; p < 0.001). Treatment with erythromycin for 2 wk did not alter the nasal NO in four control subjects. DPB is the third pulmonary disease in which nasal NO is low. The reduced nasal NO may well be involved in the pathogenesis of DPB, and NO measurements may serve as a noninvasive test in the diagnosis of DPB.

A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after a numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from the optimized linear combination of retained states in the truncated Hilbert space with a numerically chosen basis. This algorithm does not suffer from the negative sign problem and can be applied to any type of Hamiltonian in any dimension. The efficiency is tested in examples of the Hubbard model where the basis of Slater determinants is numerically optimized. We show results on fast convergence and accuracy achieved with a small number of retained states.

We investigate the doping of a two-orbital chain with mobile S = 1/2 fermions as a valid model fur Y2-xCaxBaNiO5. The S = 1 spins are stabilized by strong, ferromagnetic Hund's rule couplings, We calculate correlation functions and thermodynamic quantities by density matrix renormalization group methods and find a new hierarchy of energy scales in the spin sector upon doping. Capless spin excitations are generated at a lower energy scale by interactions among itinerant polarons created by each hole and coexist with the larger scale of the gapful spin-liquid background of the S = 1 chain accompanied by a finite string order parameter.

Pseudogap phenomena in high-T-c cuprates are examined. The effective action for 2D electron systems with antiferromagnetic (AFM) and d(x2-y2)-wave superconducting (dSC) fluctuations is considered. By the SCR (self-consistent renormalization), the spin and the pairing correlation lengths, xi(sigma) and xi(d), and 1/T-1 T are calculated. The pseudogap (PG) emerges when dSC short-range order (SRO) dominates over AFM-SRO. When damping for the spin wave strongly ;depends on xi(d) through the formation of precursor singlets around (pi, 0) and (0, pi) points, the spin PG in underdoped cuprates is reproduced. Otherwise. the PG region shrinks as in overdoped cuprates. (C) 2000 Elsevier Science B.V. All rights reserved.

To understand the incoherent optical response of La1-xSrxMnO3 in the ferromagnetic and metallic phase near the metal-insulator transition, we examine the effects of e(g)-orbital degeneracy, Coulomb interactions, and Jahn-Teller distortions under the perfect polarization of spins, employing the Lanczos diagonalization method. Orbital fluctuations by the Coulomb interaction induce a large and broad structure of the incoherence and suppress Drude weight. The Jahn-Teller distortions work cooperatively to enhance this incoherence. (C) 2000 Elsevier Science B.V. All rights reserved.

Resistance-shunted Josephson junctions are studied theoretically based on a tight-binding model. In addition to the effective bandwidth 2h Delta(eff), this multi-level system genuinely has a novel crossover at lower energy Kh Delta(eff) below which the density of states becomes strongly degenerate, where K is a dimensionless damping strength. The optical responses take nearly Lorentzian forms with a width of the order of Kh Delta. The non-linear I-V characteristics is also discussed. (C) 2000 Elsevier Science B.V. All rights reserved.

The doping of a two-orbital chain with mobile S = 1/2 fermions and strong Hund's rule couplings stabilizing the S = 1 spins strongly depends on the presence of a level difference among these orbitals. Using density matrix renormalization group (DMRG) methods, we find a finite spin gap upon doping and dominant pairing correlations without level difference, whereas the presence of a level difference leads to dominant charge density wave (CDW) correlations with gapless spin-excitations. The string correlation function also shows qualitative differences between the two models.

The properties and mechanism of the magnetic phase transition of the perovskite-type Ti oxides, which is driven by the Ti-O-Ti bond angle distortion. are studied theoretically using the effective spin and pseudo-spin Hamiltonian with strong Coulomb repulsion. It is shown that the A-type antiferromagnetic (AFM(A)) to ferromagnetic (FM) phase transition occurs as the Ti-O-Ti bond angle is decreased. Through this phase transition, the orbital state is hardly changed so that the spin-exchange coupling along the c-axis changes nearly continuously from positive to negative and is approximately zero at the phase boundary. The resultant strong two-dimensionality in the spin coupling causes rapid suppression of the critical temperature, as observed experimentally.

We study the pseudogap phenomena in the single-particle excitations in high-T-c cuprates. based on the mode-mode coupling theory of antiferromagnetic (AFM) and d(x2-y2)-wave superconducting (dSC) fluctuations. For the parameter values for underdoped cuprates. pseudogap structure develops in the single-particle excitations around (pi,0) and (0,pi) points below the pseudo-spin-gap temperature T-PG Signaled by the reduction of low-energy spin correlations, while the calculated results for the overdoped cuprates show no clear pseudogap, in qualitative agreement with the experimental data. (C) 2000 Elsevier Science B.V. All rights reserved.

Single-electron spectral function and d-wave pairing correlations are calculated for the 2D t-J model by exact diagonalization including distant single-electron hoppings and three-site pair hoppings. We show that the (pi,0)-level position has a substantial effect on the pairing correlations. It is also suggested that the experimentally observed deep (pi,0)-level is due to the pairing interaction itself. We demonstrate that further enhancement of superconductivity could be achieved by the level tuning through distant hoppings. (C) 2000 Elsevier Science B.V. All rights reserved.

Proposals to enhance the spin excitation gap and the pairing correlations in doped Mott insulators are reviewed. Design and tuning of flat dispersions near the Fermi level extend the critical region of the metal-to-Mott insulator transition thereby inducing stronger pairing instabilities. Several one- and two-dimensional decorated lattices are studied. We also discuss the tuning for stronger d-wave pairing instabilities in a microscopic model of high-T-c cuprates. (C) 2000 Elsevier Science B.V. All rights reserved.

A minimal model is proposed for the perovskite manganese oxides showing strongly incoherent charge dynamics with a suppressed Drude weight in the ferromagnetic and metallic phase near the insulator. We investigate a generalized double-exchange model which includes three elements; the orbital degeneracy of e(g) conduction bands, the Coulomb interaction and fluctuating Jahn-Teller distortions. We demonstrate that Lanczos diagonalization calculations combined with Monte Carlo sampling of the largely fluctuating lattice distortions result in the optical conductivity which quantitatively accounts for the experimental indications. It is found that all three elements are indispensable for understanding the charge dynamics in these compounds.

We analyze pseudogap phenomena widely observed in the underdoped cuprates. We assume the existence of a strong d-wave pairing force competing with antiferromagnetic(AFM) fluctuations and the formation of hat and damped dispersion around the (pi, 0) and (0, pi) region as two important elements caused by the proximity from the Mott insulator. Using the mode-mode coupling theory for the d-wave superconducting(dSC) and AFM fluctuations, we reproduce basic properties of the pseudogap seen in the magnetic resonance, neutron scattering, angle resolved photoemission and tunneling measurements in the cuprates. Then minimal requirements to understand the pseudogap phenomena are clarified as the above two elements. A strong competition of the pairing with the antiferromagnetic fluctuations suppresses the transition temperature thereby generates the pseudogap in the underdoped region while the weakness of the AFM fluctuations leads to the absence of the pseudogap at the optimal doping concentration.

We investigate pseudogap phenomena in the 2D electron system. Based on the mode-mode coupling theory of antiferromagnetic (AFM) and d(x2-y2)-wave superconducting (dSC) fluctuations, single-particle dynamics is analyzed, For the parameter. values of underdoped cuprates, pseudogap structure grows in the single-particle spectral weight A(k, omega) around the wave vector (pi, 0) and (0, pi) below the spin pseudogap temperature T-PG Signaled by the reduction of dynamical spin correlations in qualitative agreement with the experimental data, The calculated results on A(k, omega) for the overdoped cuprates also reproduce the absence of the pseudogap in the experiments, We also discuss limitations of our mode-mode coupling approach.

Routes to enhance superconducting instability are explored for doped Mott insulators. With the help of insight for criticalities of metal-insulator transitions, geometrical design of lattice structure is proposed to control the instability. A guideline is to explicitly make flat band dispersions near the Fermi level without suppressing two-particle channels. In a one-dimensional model, numerical studies show that our prescription with finite-ranged hoppings realizes large enhancement of spin-gap and pairing dominant regions. We also propose several multiband systems, where the pairing is driven by intersite Coulomb repulsion.

We investigate the effects of suppression of single-particle dispersion near the Fermi level on the spin gap and the singlet-pairing correlation by using the exact diagonalization method for finite-size systems. We consider strongly correlated one-dimensional models, which have flat band dispersions near wave number k = pi/2, if the interactions are switched off. Our results for strongly correlated models show that the spin gap region expands as the single-particle dispersion becomes flatter. The region where the singlet-pairing correlation is the most dominant also expands in models with flatter band dispersions. Based on our numerical results, we propose a pairing mechanism induced by the flat-band dispersion.

Thermodynamics and transport properties of resistance-shunted Josephson junctions are studied theoretically in the tight-binding limit E-C/E-J much less than 1, where E-C and E-J are a charging energy and a Josephson coupling energy respectively. Based on a phenomenological harmonic-oscillator model, weak coupling region K = R-Q/R much less than 1 is analytically studied, where R and R-Q = h/(2e)(2) are a shunt resistance and the quantum resistance. In addition to an effective bandwidth 2 (h) over bar Delta(eff), we find that this multi-level system genuinely has a novel crossover at lower energy K (h) over bar Delta(eff) below which the density of states becomes strongly degenerate. These two energy scales control the linear DC responses, optical responses, and nonlinear I-V characteristics. The lower energy crossover indicates the existence of a new class of strongly-correlated phenomena beyond the framework of the Kondo problem.

A strategy to enhance d-wave superconducting correlations is proposed based on our numerical study of correlated electron models for high-T-c cuprates. We observe that the pairing is enhanced when the single-electron level around (pi, 0) is close to the Fermi lever E-F, while the d-wave pairing interaction itself contains elements to disfavor the pairing due to a shift of the (pi, 0)-level. Angle-resolved photoemission results for the cuprates are consistently explained in the presence of the d-wave pairing interaction. We propose to tune the (pi, 0)-level, under many-body effects, to E-F through optimal design of the band structure.

Roles of orbital and lattice degrees of freedom in strongly correlated systems are investigated to understand electronic properties of perovskite Mn oxides such as La1-xSrxMnO3. An extended double-exchange model containing Coulomb interaction, doubly degenerate orbitals and Jahn-Teller coupling is derived under full polarization of spins with two-dimensional anisotropy. Quantum fluctuation effects of Coulomb interaction and orbital degrees of freedom are investigated by using the quantum Monte Carlo method. In undoped states, it is crucial to consider both the Coulomb interaction and the Jahn-Teller coupling in reproducing characteristic hierarchy of energy scales among charge, orbital-lattice, and spin degrees of freedom in experiments. Our numerical results quantitatively reproduce the charge gap amplitude as well as the stabilization energy and the amplitude of the cooperative Jahn-Teller distortion in undoped compounds. Upon doping of carriers, in the absence of the Jahn-Teller distortion, critical enhancement of both charge compressibility and orbital correlation length is found with decreasing doping concentration. These are discussed as origins of strong incoherence in charge dynamics. With the Jahn-Teller coupling in the doped region, collapse of the Jahn-Teller distortion and instability to phase separation are obtained and favorably compared with experiments. These provide a possible way to understand the complicated properties of lightly doped manganites.

We discuss Mott insulating and metallic phases of a model with e(g), orbital degeneracy with regard to understanding the physics of Mn perovskite compounds. Quantum Monte Carlo (QMC) and Lanczos diagonalization (LD) results are discussed in this model. To reproduce experimental results on charge gap and Jahn-Teller distortions, we show that a synergy between the strong correlation effects and the Jahn-Teller coupling is important. The incoherent charge dynamics and strong charge fluctuations are characteristic of the metallic phase accompanied with critical enhancement of short-ranged orbital correlation near the insulator. (C) 1999 Elsevier Science S.A. All rights reserved.

The dispersion relation of a doped hole in the half-filled 2D Hubbard model is shown to follow a \k\(4) law around the (0, +/-pi) and (+/-pi,0) points in the Brillouin zone, Upon addition of pair-hopping processes this dispersion relation is unstable towards a \k\(2) law. The above follows from T = 0 Quantum Monte-Carlo calculations of the single particle spectral function A(k,omega) on 16 x 16 lattices. We discuss finite dopings and argue that the added term restores coherence to charge dynamics and drives the system towards a d(x2-y2) superconductor.

Pseudogap phenomena of high-T-c cuprates are examined. In terms of AFM (antiferromagnetic) and dSC (d(x2-y2)-wave superconducting) auxiliary fields introduced to integrate out the fermions, the effective action for 2D electron systems with AFM and dSC fluctuations is considered. By the self-consistent renormalization (SCR), the NMR relaxation rate T-1(-1), the spin correlation length xi(sigma) and the pairing correlation length xi(d) are calculated. From this calculation, a mechanism of the pseudogap formation emerges as the region of dominant d-wave short-range order (SRO) over AFM-SRO. When damping for the AFM fluctuation strongly depends on the dSC correlation length through the formation of precursor singlets around (pi, 0) and (0, pi) points in the momentum space, the pseudogap appears in a region of the normal state characterized by decreasing 1/T1T and increasing AFM correlation length with decrease in temperature. This reproduces a characteristic feature of the pseudogap phenomena in many underdoped cuprates. When the damping becomes insensitive to the dSC correlation length, the pseudogap region shrinks as in the overdoped cuprates.

Taking the orbital degeneracy of e(g) conduction bands and the Coulomb interaction into account in a double-exchange model, we investigate the charge dynamics of perovskite Mn oxides by the Lanczos diagonalization method. In the metallic phase near the Mott insulator, it is found that the optical conductivity for a spin-polarized two-dimensional system exhibits a weight transfer to a broad and incoherent structure within the lower-Hubbard band together with a suppressed Drude weight. It reproduces a qualitative feature of the experimental results. As an orbital effect, we find that an anomalous charge correlation at quarter filling suppresses the coherent charge dynamics and signals precursor to the charge ordering.

Charge dynamics of the two-dimensional Hubbard model is investigated.
Lancz$\ddot{\rm o}$s-diagonalization results for the optical conductivity and
the Drude weight of this model are presented. Near the Mott transition, large
incoherence below the upper-Hubbard band is obtained together with a remarkably
suppressed Drude weight in two dimensions while the clearly coherent character
is shown in one dimension. The two-dimensional results are consistent with
previous results from quantum Monte Carlo calculations indicating that the Mott
transition in this two-dimensional model belongs to the universality class
characterized by the dynamical exponent of $z=4$.

Thermodynamics and transport properties of a dissipative carrier are studied based on the Caldeira-Leggett phenomenological theory. A weak coupling theory is constructed to study the crossover behavior between the low-temperature and the high-temperature region. We found that the coherent part of the optical mobility disappears for 0 < s < 2, where s is all exponent of a spectral function of the environment. Detailed calculation is performed for ohmic clamping (s = 1). In this case, the specific heat shows unusual T-linear behavior, and the optical mobility takes a non-Drude form el en at zero temperature.

Roles of Coulomb interaction, orbital degeneracy and Jahn-Teller coupling in double-exchange models are examined for perovskite Mn oxides. We study the undoped insulator as well as metal-insulator transitions by hole doping, and especially strong incoherence of ferromagnetic metal. We derive models where all the spins are fully polarized in two-dimensional planes as indicated by experimental results, and investigate their ground-state properties by the quantum Monte Carlo method. At half filling where the number of e(q) electrons is one per site on average, the Coulomb interaction opens a Mott gap and induces a staggered orbital ordering. The opening of the gap is, however, substantially slower than the mean-field results if the Jahn-Teller coupling is absent. The synergy between the strong correlation and the Jahn-Teller coupling largely enhances the charge gap amplitude and reproduces realistic amplitudes and stabilization energy of the Jahn-Teller distortion. Doping of carriers destroys the orbital ordering stabilized by the Coulomb interaction. The short-ranged orbital correlation is critically enhanced in metals toward the metal-insulator transition, which should be related to the strong incoherence of charge dynamics observed in experiments. Our model, moreover exhibits a uniform ordering of d(x)2(-y)2 orbitals over a wide region of doping in agreement with experimental indications.

Metal-insulator transitions are accompanied by huge resistivity changes, even over tens of orders of magnitude, and are widely observed in condensed-matter systems. This article presents the observations and current understanding of the metal-insulator transition with a pedagogical introduction to the subject. Especially important are the transitions driven by correlation effects associated with the electron-electron interaction. The insulating phase caused by the correlation effects is categorized as the Mott Insulator. Near the transition point the metallic state shows fluctuations and orderings in the spin, charge, and orbital degrees of freedom. The properties of these metals are frequently quite different from those of ordinary metals, as measured by transport, optical, and magnetic probes. The review first describes theoretical approaches to the unusual metallic states and to the metal-insulator transition. The Fermi-liquid theory treats the correlations that can be adiabatically connected with the noninteracting picture. Strong-coupling models that do not require Fermi-liquid behavior have also been developed. Much work has also been done on the scaling theory of the transition. A central issue for this review is the evaluation of these approaches in simple theoretical systems such as the Hubbard model and t-J models. Another key issue is strong competition among various orderings as in the interplay of spin and orbital fluctuations.Experimentally, the unusual properties of the metallic state near the insulating transition have been most extensively studied in d-electron systems. In particular, there is revived interest in transition-metal oxides, motivated by the epoch-making findings of high-temperature superconductivity in cuprates and colossal magnetoresistance in manganites. The article reviews the rich phenomena of anomalous metallicity, taking as examples Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Ru compounds. The diverse phenomena include strong spin and orbital fluctuations, mass renormalization effects, incoherence of charge dynamics, and phase transitions under control of key parameters such as band filling, bandwidth, and dimensionality. These parameters are experimentally varied by doping, pressure, chemical composition, and magnetic fields. Much of the observed behavior can be described by the current theory. Open questions and future problems are also extracted from comparison between experimental results and theoretical achievements. [S0034-6861(98)00103-2].

Ground state properties of multi-orbital Hubbard models are investigated by the auxiliary field quantum Monte Carlo method. A Monte Carlo technique generalized to the multi-orbital systems is introduced and examined in detail. The algorithm contains non-trivial cases where the negative sign problem does not exist. We investigate one-dimensional systems with doubly degenerate orbitals by this new technique. Properties of the Mott insulating state are quantitatively clarified as the strongly correlated insulator, where the charge gap amplitude is much larger than the spin gap. The insulator-metal transitions driven by the chemical potential shows a universality class with the correlation length exponent nu = 1/2, which is consistent with the scaling arguments. Increasing level split between two orbitals drives crossover from the Mott insulator with high spin state to the band insulator with low spin state; where the spin gap amplitude increases and becomes closer to the charge gap. Experimental relevance of our results especially to Haldane materials is discussed.

Thermodynamics and transport properties of a dissipative particle in a tight-binding model are studied through specific heat and optical conductivity. A weak coupling theory is constituted to study the crossover behavior between the low-temperature region and the high-temperature region analytically. We found that coherent part around zero frequency in the optical conductivity disappears for 0 < s < 2, where s is an exponent of a spectral function of the environment. Detailed calculation is performed for ohmic damping (s = 1). In this case, the specific heat shows an unusual T-linear behavior at low temperatures, which indicates that the environment strongly influences the particle motion, and changes the low-energy states of the dissipative particle. The optical conductivity sigma(w) takes a non-Drude form even at zero temperature, and the high-frequency side behaves as omega(2K-2): where K is a dimensionless damping strength. The high frequency side of the optical conductivity is independent of temperatures, while the low frequency side depends on the temperature, and behaves as T2K-2 at high temperatures. We also comment on the application of this model to the description of incoherent motion in correlated electron systems.

We show numerically that the nature of the doping-induced metal-insulator transition in the two-dimensional Hubbard model with hopping matrix element t and Coulomb repulsion U is radically altered by the inclusion of a term W that depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length xi(l), in the insulating state. At W/t = 0.05 and U/t = 4, we find results consistent with xi(l)similar to\mu - mu(c)\(-1/2) where mu(c) is the critical chemical potential. In contrast, xi(l)similar to\mu - mu(c)\(-1/4) for the Hubbard model at U/t = 4, At half-filling, we calculate the density of states N(omega). The large value of N(omega) in the vicinity of w = mu(c) present at W = 0 is suppressed with growing values of W. At finite doping, the d-wave pair-field correlations are enhanced with growing values of W. The numerical results imply that at finite values of W doping the antiferromagnetic Mott insulator leads to a d(x2-y2) superconductor.

Drude weight of optical conductivity is calculated at zero temperature by exact diagonalization for the two-dimensional t-J model with the two-particle term, W. For the ordinary t-J model with W = 0, the scaling of the Drude weight D proportional to delta(2) for small doping concentration delta is obtained, which indicates anomalous dynamic exponent z = 4 of the Mtt transition. When W is switched on, the dynamic exponent recovers its conventional. value z = 2 . This corresponds to an incoherent to-coherent transition associated with the switching of the two-particle transfer.

Effects of possible orbital order in magnetic properties of two-dimensional spin gap system fur CaV4O9 are investigated theoretically. After analyzing experimental data, we show that single orbital models assumed in the literature are insufficient to reproduce the data. To understand the origin of the discrepancy, we assume that in d(1) state of V, d(chi 2) and d(yz) orbitals have substantial contributions in the lowest-energy atomic level which leads to a double-degeneracy. We study possible configurations of the orbital order. By exact diagonalization and perturbation expansion, we calculate the susceptibility, wavenumber dependence of low-lying excitations and equal-time spin-spin correlations which is related to integrated intensity of the neutron inelastic scattering. These quantities sensitively depend on the configuration of the orbital order. The calculated results for some configurations of the orbital order reproduce many experimental results much better than the previous single-orbital models. However some discrepancy still remains to completely reproduce all of the reported experimental results. To understand the origin of these discrepancies, we point out the possible importance of the partially occupied d(chi)y orbital in addition to orbital order of partially filled d(chi z) and d(yz) orbitals.

The roles of orbital order in magnetic properties of two-dimensional spin-gap system for CaV4O9 are investigated theoretically. We assume that one of the doubly degenerated d(xz) and d(yz) orbitals is occupied in d(1) state of V. We consider several models with possible orbital orders. The strengths of the spin-exchange couplings for each model are determined to reproduce the temperature dependence of the uniform magnetic susceptibility in experiments by using the exact diagonalization. By the perturbation expansion, we calculate the energy dispersion of low-lying excitations and the integrated intensity of the neutron inelastic scattering. These quantities sensitively depend on the types of the orbital order. The origin of the spin gap for these models is ascribed to a generalized four-spin singlet. Although none of the models is complete to reproduce all of the reported experimental results, we point out basic mechanisms to reproduce each experimental result. (C) 1998 Elsevier Science B.V. All rights reserved.

Small Drude weight D together with small specific heat coefficient gamma observed in the ferromagnetic phase of R(1-x)A(x)MnO(3) (R = La, Pr, Nd, Sm; A = Ca; Sr, Ba) are analyzed in terms of a proximity effect of the Mott insulator. The scaling theory for the metal-insulator transition with the critical enhancement of orbital correlations toward the staggered ordering of two e(g) orbitals such as 3x(2) - r(2) and 3y(2) - r(2) symmetries may lead to the critical exponents of D proportional to delta(u) and gamma proportional to delta(v) with u = 3/2 and v = 0. The result agrees with the experimental indications.

To the Hubbard model on a square lattice we add an interaction W that depends upon the square of a near-neighbor hopping. We use zero-temperature quantum Monte Carlo simulations on lattice sizes up to 16 x 16, to show that at half-filling and constant value of the Hubbard repulsion, the interaction W triggers a quantum transition between an antiferromagnetic Mott insulator and a d(x2-y2) superconductor. With a combination of finite-temperature quantum Monte Carlo simulations and the maximum entropy method, Eve study spin and charge degrees of freedom in the superconducting state. We give numerical evidence for the occurrence of a finite-temperature Kosterlitz-Thouless transition to the d(x2-y2) superconducting state. Above and below the Kosterlitz-Thouless transition temperature, T-KT, We compute the one-electron density of states N(omega), the spin relaxation rate 1/T-1, as well as the imaginary ad real part of the spin susceptibility chi((q) OVER RIGHT ARROW, omega). The spin dynamics are characterized by the vanishing of 1/T-1 and divergence of Re chi((q) OVER RIGHT ARROW = (pi, pi), omega = 0) in the low-temperature limit. As T-KT is approached N(omega) develops a pseudogap feature and below T-KT Im chi((q) OVER RIGHT ARROW = (pi, pi), omega) shows a peak at finite frequency.

We have performed a large scale quantum Monte Carlo study of the quantum phase transition in a planar spin-1/2 Heisenberg antiferromagnet with CaV4O9 structure. We obtain a dynamical exponent z = 1.018 +/- 0.02, consistent with Lorentz invariance. The critical exponents beta, nu and eta agree within our errors with the classical 3D O(3) exponents, expected from mapping to the nonlinear sigma model.

I review recent progress in understanding metal-insulator transitions of strongly correlated electron systems. In particular, using improved algorithms of quantum Monte Carlo calculations, the universality class of the transition between the Mott insulator and metals in two dimensions has been clarified and analyzed numerically and compared with the prediction from the scaling theory. It shows the existence of new universality class of the metal-insulator transition characterized by unusual suppression of coherence in the metallic side due to a large dynamical exponent. Its relevance to understand the unusual metallic states near the Mott insulator widely observed in transition metal compounds such as high-Tc cuprates and manganites is discussed.

The conductivity and Hall coefficient for various types of t-J ladders are calculated as a function of temperature and frequency by numerical diagonalization. A crossover from incoherent to coherent charge dynamics is found at a temperature T-coh There exists another crossover at T-PG below which a pseudogap opens in the optical spectra, induced by the opening of a spin gap. Ln the absence of the spin gap, T-coh and the coherent weight are suppressed especially with increasing dimensionality. On lire contrary, T-coh, is strongly enhanced by the pseudogap formation below T-PG, whereas the coherent Drude weight decreases with increasing dimensionality. The Hall coefficient shows a strong crossover at T-PG below which it has large amplitude for small doping concentration.

We present a framework of an auxiliary field quantum Monte Carlo (QMC) method for multiorbital Hubbard models. Our formulation can he applied to a Hamiltonian which includes terms for on-site Coulomb interaction for both intra- and inter-orbitals, intra-site exchange interaction and energy differences between orbitals. Based on our framework, we point out possible ways to investigate various phase. transitions such as metal-insulator. magnetic and orbital order-disorder transitions without the minus sign problem. As an application, a two-band model is investigated by the projection QMC method and the ground state properties of this model are presented.

We study a current-biased 0-pi-0 Josephson junction made by high-T-c superconductors, theoretically. When a length of the pi junction is large enough, this junction contains a vortex-antivortex pair at both ends of the pi junction. Magnetic flux carried by the vortices is calculated using the sine-Gordon equation. The result shows that the magnetic flux of the vortices is suppressed to zero as the distance between the vortices is reduced. By applying an external current, the orientation of the vortices is reversed, and a voltage pulse is generated. The current needed for this transition and generated pulse energy are calculated. Macroscopic quantum tunneling (MQT) in this transition is also studied. The tunneling rate has been evaluated by an effective Hamiltonian with one degree of freedom.

We study effects of interladder coupling on critical magnetic properties of spin ladder systems doped with small concentrations of nonmagnetic impurities, using the scaling theory together with quantum Monte Carlo (QMC) calculations. Scaling properties in a wide region in the parameter space of the impurity concentration x and the interladder coupling are governed by the quantum critical point (QCP) of the undoped system for the transition between antiferromagnetically ordered and spin-gapped phases. This multi-dimensional and strong-coupling region has characteristic power-law dependences on x for magnetic properties such as the Neel temperature. The relevance of this criticality for understanding experimental results of ladder compounds is stressed.

Effects of nonmagnetic impurity doping on an antiferromagnetic spin-1/2 Heisenberg ladder system are studied by the quantum Monte Carlo method. A single nonmagnetic impurity induces a localized spin-1/2 moment accompanied by static and enhanced antiferromagnetic correlations around it. A small and finite concentration of impurities induces a remarkable change of magnetic and thermodynamic properties with gapless excitations. It also shows rather sharp but continuous crossover around a impurity concentration of about 4%. Above the crossover concentration, all the spins are strongly coupled, participating in the enhanced and rather uniform power-law decay of the antiferromagnetic correlation. Below the crossover concentration, each impurity forms an antiferromagnetically correlated cluster only weakly coupled each other. For random distribution of impurities, large Curie-like susceptibility accompanied with small residual entropy is obtained at low temperatures, in agreement with recent experimental observation in Zn-doped SrCu2O3 The temperature dependence of antiferromagnetic susceptibility shows power-law-like but weaker divergence than the single chain antiferromagnet in the temperature range studied.

Effects of nonmagnetic impurity doping in a spin ladder system with a spin gap are investigated by the exact diagonalization and the variational Monte Carlo calculations. Small amount of impurity doping generates a nearly free spin bound to each impurity. These nearly free spins interact each other only weakly giving rise to gapless spin excitations. Another important aspect is that short-ranged antiferromagnetic correlation is enhanced especially around the impurity sites. We propose a possible scenario for this drastic change in the spin gapped ladder system. We also compare with the experimental results of Zn-doped SrCu2O3.

We consider a Hubbard model on a square lattice with an additional interaction, W, which depends upon the square of the near-neighbor hopping. At half filling and a constant value of the Hubbard repulsion, increasing the strength of the interaction W drives the system from an antiferromagnetic Mott insulator to a d(x2-y2) superconductor. This conclusion is reached on the basis of zero temperature quantum Monte Carlo simulations on lattice sizes up to 16 x 16.

Macroscopic quantum tunneling (MQT) for a single fluxon moving along a long Josephson junction is studied theoretically. To introduce a fluxon-pinning force, we consider inhomogeneities made by modifying thickness of an insulating layer locally. Two different situations are studied: one is the quantum tunneling from a metastable state caused by a single inhomogeneity, and the other is the quantum tunneling in a two-state system made by two inhomogeneities. In the quantum tunneling from a metastable state, the decay rate is estimated within the WKB approximation. Dissipation effects on a fluxon dynamics are taken into account by the Caldeira-Leggett theory. We propose a device to observe quantum tunneling of a fluxon experimentally. Required experimental resolutions to observe MQT of a fluxon seem attainable within the presently available micro-fabrication technique. For the two-state system, we study quantum resonance between two stable states, i.e., macroscopic quantum coherence (MQC). From the estimate for dissipation coefficients due to quasiparticle tunneling, the observation of MQC appears to be possible within the Caldeira-Leggett theory.

Various types of superfluid-insulator transitions are investigated for two-component lattice boson systems in two dimensions with on-site hard-core repulsion and the component-dependent intersite interaction. The mean-field phase diagram is obtained by the Gutzwiller-type variational technique. Various ground-state properties are also studied by the quantum Monte Carlo method. Our model exhibits two types of diagonal long-range orders; the density order around the density n = 1/2 and the Ising-type component order near n = 1. In contrast to the Gutzwiller results, the Monte Carlo results show that the continuous growth of the component correlation severely suppresses the superfluidity as well as the inverse of the effective mass in the critical region of the component order transition. We propose a mechanism of this mass enhancement observed even far from the Mott insulating filling n = 1, when the Ising-type component order persists into n not equal 1. Possible relevance of this type of mass enhancement in other systems is also discussed.

We study the filling-controlled metal-insulator transition in the
two-dimensional Hubbard model near half-filling with the use of zero
temperature quantum Monte Carlo methods. In the metallic phase, the
compressibility behaves as $\kappa \propto |\mu - \mu_c|^{-0.58\pm0.08}$ where
$\mu_c$ is the critical chemical potential. In the insulating phase, the
localization length follows $\xi_l \propto |\mu - \mu_c|^{-\nu_l}$ with $\nu_l
= 0.26 \pm 0.05$. Under the assumption of hyperscaling, the compressibility
data leads to a correlation length exponent $\nu_\kappa = 0.21 \pm 0.04$. Our
results show that the exponents $\nu_\kappa$ and $\nu_l$ agree within
statistical uncertainty. This confirms the assumption of hyperscaling with
correlation length exponent $\nu = 1/4$ and dynamical exponent $z = 4$. In
contrast the metal-insulator transition in the generic band insulators in all
dimensions as well as in the one-dimensional Hubbard model satisfy the
hyperscaling assumption with exponents $\nu = 1/2$ and $z = 2$.

Asymptotic properties of nearly half-filled one-dimensional conductors coupled with phonons are studied through a renormalization-group method. Due to spin-charge coupling via an electron-phonon interaction, the spin correlation varies with filling as well as the charge correlation. Depending on the relation between cutoff energy scales of the umklapp process and of the electron-phonon interaction, various phases appear. We find a metallic phase with a spin gap and a dominant charge-density-wave correlation near half filling between a gapless density-wave phase (like in the doped repulsive Hubbard model) and a superconductor phase with a spin gap. The spin gap is produced by phonon-assisted backward scatterings that interfere with the umklapp process constructively or destructively depending on the character of electron-phonon coupling.

Effects of nonmagnetic impurity doping in a spin ladder system with a spin gap are investigated by exact diagonalization and variational Monte Carlo calculations. Substantial changes in macroscopic properties such as enhancements in spin correlations and magnetic susceptibilities are observed in the low impurity concentration region, which are due to an increase of low-energy states. These results suggest that a small but finite amount of nonmagnetic impurity doping causes reduction or disappearance of the spin gap. This qualitatively explains the experimental results for Zn-doped SrCu2O3 in which a small amount of doping results in disappearance of the spin gap. We propose a possible scenario for this marked change as a quantum phase transition in a spin-gap ladder system due to spinon doping effects.

Mechanisms of spin-gap formation in two-dimensional Mott insulators are investigated. The origin of the spin gap is analyzed as a dimer gap in generalized Heisenberg models with dimerization, while it is interpreted as the plaquette singlet gap in Ca(V)4O(9).

We numerically calculate the high-frequency Hall coefficient, R(H), for the 2D Hubbard model at small hole-doping near half-filling. In the weak-coupling regime R(H) is electron-like and comparable to its U/t=0 value. In the strong-coupling regime, where the mapping onto the t-J model is justified, R(H) is electron-like with small amplitude in the temperature regimes T > U, T < J, and hole-like in the temperature regime J < T < U. Our conclusions are consistent with the picture of a Mott transition driven by the divergence of the effective mass as opposed to the vanishing of the number of charge carriers. This conclusion is valid in the strong- and weak-coupling regimes.

The temperature and the doping concentration dependences of the equal time spin correlation, S(Q), are calculated by a quantum Monte Carlo method, and are analyzed by introducing a doping-dependent intrinsic correlation length and a thermal correlation length in a phenomenological way. This provides a unified picture of the spin correlation in the small-doping and low-temperature region.

Renormalization-group equations are solved to study phase diagrams of nearly-half-filled one-dimensional conductors interacting with phonons. A spin-gap charge density wave phase exists between a gapless density wave phase and a spin-gap superconductor phase. On-site and intersite electron-phonon couplings show large differences near half-filling in the presence of on-site electron repulsion.

Continuous transitions between a Mott insulator and a correlated metal are studied with the scaling theory. The validity of hyperscaling analysis is examined. As an example of the criticality, two-dimensional He-3 systems near the Mott transition observed experimentally are analyzed in favor of the mass singularity in the form m* alpha delta(-1) where delta is the density of He-3 measured from the Mott insulator. Several consequences of the scaling theory are derived when the metallic state is described by the Fermi liquid. The breakdown of the Fermi liquid towards the transition point is figured out in this framework.

We use quantum Monte Carlo methods to determine T = 0 Green functions, G((r) over right arrow,omega), on lattices up to 16 x 16 for the 2D Hubbard model at U/t = 4. For chemical potentials mu within the Hubbard gap \mu\ < mu(c) and at long distances (r) over right arrow, G((r) over right arrow, omega = mu) similar to e(-\(r) over right arrow\/xi l) with critical behavior xi(l) similar to \mu - mu(c)\(-nu), nu = 0.26 +/- 0.05. This result stands in agreement with the assumption of hyperscaling with correlation exponent nu = 1/4 and dynamical exponent z = 4. In contrast, the generic band insulator as well as the metal-insulator transition in the 1D Hubbard model are characterized by nu = 1/2 and z = 2.

The exponents of spin and charge correlations of one-dimensional electron systems are calculated by a renormalization-group method. We study combined effects of electron-phonon interaction and the Umklapp process on renormalization flows. As scattering processes are successively integrated out, these two processes are interfered with each other depending on the type of electron-phonon coupling, phonon frequency and filling. We demonstrate how these factors control a spin gap formation and density-wave/superconductor correlations.

We present a numerically stable Quantum Monte Carlo algorithm to calculate zero-temperature imaginary-time Green functions G(r, tau) for Hubbard type models. We illustrate the efficiency of the algorithm by calculating the on-site Green function G(r = 0, tau) on 4 x 4 to 12 x 12 lattices for the two-dimensional half-filled repulsive Hubbard model at U/t = 4. By fitting the tail of G(r = 0, tau) at long imaginary time to the form e(-tau Delta c), we obtain a precise estimate of the charge gap: Delta(c) 0.67 +/- 0.02 in units of the hopping matrix element. We argue that the algorithm provides a powerful tool to study the metal-insulator transition from the insulator side.

We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV4O9. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.

We investigate temperature dependence of spin correlations in the one-dimensional Hubbard model at or close to half filling by the quantum Monte Carlo method. The numerical data are analyzed by introducing a crossover generated from an interplay of the intrinsic correlation length and the thermal correlation length. It provides a unified picture of the spin correlation of the metallic phase near the Mott insulator at finite temperatures. Our results show that the crossover, not taken account by the conventional renormalization group and the conformal field theory, becomes more and more important to understand the spin correlation near the Mott transition point.

Transitions between the Mott insulator and metals in clean systems are analyzed with the scaling theory in terms of quantum critical phenomena. In the case of generic transitions controled by the filling, the scaling theory is established from analyses of the Drude weight and the compressibility based on hyperscaling. In the transition to the Mott insulator, a new universality class with the correlation length exponent v<1/2 and the dynamical exponent z>2 is derived, which is in contrast to the transition to the band insulator characterized by v=1/2 and z=2. The unusual exponents lead to various anomalous characters of metals near the Mott insulator such as strong suppression of the degeneracy temperature, and nonlinear dependence of the Drude weight on the doping concentration. Remarkable properties are also found in the specific heat, the compressibility and spin correlations. A mechanism of high temperature superconductivity is discussed in terms of the release from the suppressed coherence.

We calculate with quantum Monte Carlo methods the Hall coefficient RH for the 2D Hubbard model at small hole doping near half filling. In the weak coupling regime RH is electronlike. In the strong coupling regime, where the mapping to the t- J model is justified, RH is electronlike with small amplitude in the temperature regime T>U, T<J and holelike in the temperature regime J<T<U. Our results are consistent with the picture of a Mott transition driven by the divergence of the effective mass as opposed to the vanishing of the number of charge carriers. © 1995 The American Physical Society.

Anomalous metallic states near the Mott insulator are analyzed in terms of the critical scaling toward the metal-insulator transition. Continuous transitions from a metal to the Mott insulator are characterized either by the mass divergence as in the bi-component systems or the vanishing carrier number as in the valence bond systems. A set of critical exponents in these two cases is deduced from the sealing theory. The correlation exponent v and the dynamical exponent z satisfy v = 1/2d and z = 2d when the mass diverges in d dimensions, while v = 1/2 and z = 2 if the carrier number vanishes. Crossovers between quantum critical regime and thermal critical regime inferred from this theory shed light on understanding experimental indications in high-T-c cuprates and other strongly correlated systems.

Spill and charge responses of the normal state in the cuprates are analyzed is terms of a state close to the Mott insulator. An anomalous feature of the cuprates is demonstrated from a general theory of the Mott transition. A remarkable crossover between a single- and a multi-component carrier system and its consequences in the cuprates is discussed. A phenomenological theory of the spin correlation is also constructed based on the fact that the spin correlation has a characteristic correlation length inversely proportional to the doping concentration with an insensitive temperature dependence. The NMR and the neutron data of the cuprates are both accounted for by the phenomenological theory.

The spectrum of charge excitations, ImN(qt ω) has been evaluated near the Mott transition in the one-dimensional Hubbard model with a particular value of the Coulomb interaction. The present theory based on a continuum limit describes the smooth change between the Tomonaga-Luttinger liquid state with a q-linear mode and the Mott insulator with a charge gap, by considering Umklapp scattering. The charge susceptibility is seen to diverge proportional to the inverse of the doping rate as the Mott insulator state is approached, in agreement with Bethe-ansatz result. It is shown that the q region where the renormalization group theory and conformal field theory are valid becomes vanishingly small as the transition is approached. © 1994, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The quantum phase transition between a spin gap state and an antiferromagnetic phase is investigated. We study S=1/2 antiferromagnetic Heisenberg chains coupled by antiferromagnetic interchain interaction. The intrachain exchanges have alternating strength. The phase boundary between the antiferromagnetically ordered phase and a spin gap phase is also obtained in a parameter space of the amplitude of the interchain coupling and the dimerization. The spin-wave approximation substantially overestimates the antiferromagnetic phase. The competition between the long range order and the spin gap is examined in detail. We estimate a variety of critical exponents at the transition, namely, exponents v, θ and z defined as the exponent of the correlation length, the magnetization curve and the dynamical exponent, respectively. From the quantum Monte Carlo simulation, the exponents v, θ and z are estimated to be unity. The exponents v and θ are different from the estimated values in one dimension. It suggests that the universality changes due to the dimensionality change. In our estimates, the exponent v does not agree with the prediction from three dimensional classical Heisenberg model. We also discuss the relevance of our result to spin-Peierls systems with lattice distortion. © 1994, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Critical properties of transitions between a variety of quantum fluids and the Mott insulator are examined in terms of the transition to an incompressible state. In one dimension, they show universally common properties each other irrespective of the statistics, components and the interaction of particles. In two dimensions, they show qualitative differences originated from the differences in the nature of the quantum fluid. It is useful to categorize the singularity at the Mott transition into two types, namely, one characterized by the charge mass divergence and the other by the vanishment of the carrier number. This difference originates from the number of components. Its variety is further explored by examining various cases such as strongly correlated fermions, hard core bosons and boson t-J models. Critical properties to other incompressible states such as spin gap states and the fractional quantum Hall state are also discussed from the same viewpoint. Relevance of our analyses to the understanding of normal state properties in high-Tc cuprates and other transition metal oxides is discussed. © 1994, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

a phenomenological theory of the antiferromagnetic correlations in cuprates is constructed from analyses of recent numerical results of the Hubbard model. Two crossover temperatures are predicted to exist. In three regions divided by the two crossover temperatures, we present a qualitative but explicit form of doping and temperature dependences of the dynamical susceptibility χ(q, ω), which agrees with NMR and neutron scattering data of cuprates. It solves recent controversy between these two experimental results and provides us with a unified picture of antiferromagnetic correlation in cuprates. © 1994, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Critical properties of the transition between the Mott insulator and quantum fluids are investigated by using the scaling theory. The Mott insulating phase and the quantum fluid phase of bi-component systems are categorized into several types depending on the existence of order and the type of excitation spectra. The critical exponents of the transition in multicomponent systems are discussed for various combinations of metal-insulator and superfiuid-insulator transitions. For the generic transition between a genuinely multicomponent metal and the Mott insulator in d dimensions, the hyperscaling is satisfied with the correlation exponent v = 1/2d, the dynamical exponent z=2d, and the Drude weight exponent [formula omitted]. It is argued that the upper critical dimension dc satisfies dc≥2. The above exponents are compared with v=l/2, z=2t and ≥ for the transition to the band insulator. Critical properties of the energy gap, the compressibility and other quantities are also discussed. © 1994, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Two-dimensional Hubbard model with both nearest- and next-nearest-neighbor transfers is studied. A singularity in the charge susceptibility at the Mott transition point is observed, leading to the anomaly of the charge mass mx in the form mtoz\Sr\where S is the doping concentration. The singularity is similar to that in the case without the next-nearest-neighbor transfer. This indicates that the singularity in the charge mass is a universal nature of this model, irrespective of its band structure. © 1993, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The ground state energy, the energy gap and the Fourier transform of the staggered spin correlation function S(Q) at zero temperature are investigated for the 5=1/2 antiferromagnetic Heisenberg model on a dimerized square lattice with the help of the spin-wave approximations, the second-order perturbation expansion and the quantum Monte Carlo simulations. In contrast to one-dimensional case, the spin gap appears above a finite critical value of the dimerization parameter. Sc - 0.303, where the second-order transition takes place. The antiferromagnetic long range order exists below Sc. The critical exponent of the order parameter in the antiferromagnetically ordered state is estimated by quantum Monte Carlo calculation to be -{dc∼- with B=0.27 ±0.04, while the correlation length in the spin gap region is scaled as - (S-Sc)v with v= 1.36±0.05. All of them are different from the estimates in one-dimension, v=l and the spin-wave approximation, fi=v=l. Possible relevance of our result for the spin gap behavior in high-Tc superconductors is also discussed. © 1993, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

One type of Mott transition (MTl) is characterized by diverging enhancement of the charge effective mass when one approaches a Mott insulator from the side of the paramagnetic metal. Another fundamentally different type of Mott transition (MT2) is shown to exist when a spin gap opens. The Unear coefficient of the specific heat y decreases and then vanishes at the transition point of MT2 in sharp contrast with MTl. As an example, a dimerized t-J model is shown to undergo MT2. The underlying pairing mechanism determines the character of MT2. Recent controversial experimental results on the Mott transitions in copper oxides and other strongly correlated systems are discussed from the above viewpoint. © 1993, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The phase diagram of one-dimensional dimerized t-J model is investigated by exact-diagonalization, quantum tranfer-matrix, and quantum Monte Carlo methods. The spin gap persists near but away from half-filling as well as in a strongly dimerized region, while the charge can be described as a Tomonaga-Luttinger liquid in the entire region. The spin-gap region extends to the weak-dimerization region as well as to the Haldane-gap region. Critical exponents of various correlation functions are discussed. The pairing correlation shows remarkable enhancement and by far dominates over other correlations near half-filling. At quarter filling, charge-gap formation is observed. © 1993 The American Physical Society.

The Hubbard model on a square lattice has been studied by the quantum Monte Carlo method. The nature of the Mott transition upon hole doping is investigated. Critical exponents of the metal-insulator transition estimated for charge and spin correlations are summarized. We stress that a new theoretical framework should be constructed to understand these results. Comparisons with experimental results on high-Tc oxides are also made. © 1993.

A characteristic and unique feature of electron-phonon coupling in strongly correlated metals is examined. Significant properties due to spin-Peierls fluctuation near the Mott transition recently clarified are reviewed, especially in terms of the pairing mechanism and spin gap formation in the metallic phase. A superconducting state appears when the singlet ground state of a Mott insulator with a spin gap is doped with metallic carriers. The spin-Peierls t-J model is shown to be a relevant model. Exotic features of the spin-Peierls pairing mechanism are discussed. Experimental consequences and possible relevance in high Tc oxides and fullerenes are also discussed. © 1993.

The crossover of the spin correlation function from a non-half-filled to a half-filled band is investigated for the one-dimensional Hubbard model in the ground state. For the on-site interaction U→∞, it has the form at distance r, [formula omitted] where δ is the doping concentration away from half-filling. This form determines the crossover from the asymptotic behavior ∼ 1/r1.5 away from half-filling to ∼ 1/r at half-filling. At finite U, Monte Carlo results show that the peak of the equal-time spin structure factor S (Q) scales as S (Q)∝ - 1n δ leading to the same type of crossover. A unified description of the critical exponent of the antiferromagnetic spin correlation near half-filling in one- and two-dimensional Hubbard models is given. © 1992, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Spin-fermion model on a square lattice is investigated in the perturbation expansion in terms of the spin-fermion Kondo coupling. The fermion self-energy is calculated in a selfconsistent treatment by a dominant pole approximation. The quasi-particle excitation of a doped fermion turns out to be totally incoherent. It suggests that the low energy excitations should be described by the bound state of a fermion and spins as a collective mode and imply that the fixed point of the spin-fermion model with a single fermion is the t-J model. It also suggests the spin-charge separation of the low energy excitations in the light doping region of these two models. © 1992, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The Hubbard model on a square lattice in the ground state is investigated. Various aspects of Mott transition at half-filling are clarified from the quantum Monte Carlo study. Critical exponents of the transition for charge and spin correlations are estimated. For the doping concentration ∂, the charge susceptibility is proportional to ∂ _1 indicating the divergence of charge mass for ∂→0, while the spin susceptibility is always finite and not singular near ∂=0. Several theoretical consequences of the above results are discussed. Incommensurate peak amplitude of spin correlation scales as (∂-∂C)_1 with ∂C<0.01 in disagreement with RPA results In (∂-∂c). The antiferromagnetic order at the half-filling also shows strong correlation character and is not sensitive to the shape of the fermi surface, while the incommensurate peak observed away from the half-filling is sensitively suppressed by the loss of partial nesting consistently with the weak coupling picture. Comparisons with experimental indications of high-Tc oxides are made. © 1992, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Physical properties in a dimer pairing superconductor are examined. The pairing has a finite net momentum and breaks lattice translational symmetry as well as the gauge symmetry. The mean field equations for the dimerized t-J model and the spin-Peierls t-J model are solved numerically to discuss novel features of the dimer pairing mechanism. The dynamical spin susceptibility is calculated to discuss spin excitations in the superconducting state. The energy gap opens over the Fermi surface without nodes, while the Hebel-Slichter peak is absent in the NMR relaxation rate. © 1992, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Quantum Monte Carlo results for both the repulsive and attractive Hubbard model on a square lattice are discussed. Results on pairing correlation in the repulsive Hubbard model are summarized. Momentum distribution function in the attractive Hubbard model is presented and compared with mean field results.

Optimization of the initial trial state in the ground state algorithm for the fermion simulation is performed, which quantitatively reduces the negative sign problem of the Hubbard model in two dimension. Physical quantities of the Hubbard model near half-filling are calculated.

A connection between formation of a gap in spin excitation and superconductivity is discussed in strongly correlated electron systems. A superconducting state coming from the doping of fermions into a Mott insulator with a spin gap such as dimerized spin state is investigated.

Two dimensional spin-fermion model is studied by using the perturbation method and the spin wave approximation. Non-crossing diagrams are calculated using the dominant pole approximation. As a result, we see that the renormalization parameter z is reduced as z is-proportional-to L-1/4, where L is the linear dimension of the system, and the doped fermion becomes totally incoherent in the thermodynamic limit.

Quantum Monte Carlo study of the Hubbard model on a square lattice in the ground state is reported. For the on-site interaction U=4 scaled by the transfer, the charge excitation gap at the half-filling is estimated to be δ, = 0.58±0.08. Near half-filling, the charge compressibility k follows the form k∝ δ-1 for the doping concentration δ, indicating a divergent behavior as the system approaches half-filling, while k = 0 at the half-filling. The incommensurate spin correlation length ∊ scales as [formula omitted]. © 1991, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The minus sign problem, as a problem of the non-positive-definite measure of the path integrals, is examined in the Monte Carlo simulation of the Hubbard model. A new correction method in terms of the ratio of two measured quantities is proposed to calculate physical properties. The momentum distribution and the spin correlation as well as the energy in the ground state are tested against the exactly diagonalized results. The results show that this ratio correction method is a promising prescription to reduce the minus sign problem. © 1991, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Quantum simulation algorithm for the lattice fermions in the ground state is examined. Initial trial state is optimized using the unrestricted Hartree Fock solution. Convergence to the ground state average in the projection process is compared among several choices of the trial state. The optimized trial state provides a faster convergence for physical quantities as well as a better minus sign ratio in the sampling. © 1991, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Superconducting correlation of the Hubbard model on a square lattice is reinvestigated by quantum Monte Carlo method. Results from more than one order of magnitude larger Monte Carlo steps than before are presented to discuss the convergence of the data to the ground state. By examining the dependence on the choice of initial trial states as well as on the Trotter number in detail, the superconducting correlation in the ground state is reliably obtained up to 12 × 12 lattice away from the half-filling and up to 16 x 16 lattice at the half-filling, which substantially improve former results near the half-filling. Various channels of pairing in the ground state show no system size dependence and remain quite short ranged at any filling including the region close to the half-filling. Numerical data show further evidence that neither extended s- nor d-wave superconducting state is possible in the two-dimensional Hubbard model.© 1991, THE PHYSICAL SOCIETY OF JAPAN. All Rights Reserved.

A mechanism of superconductivity coming from the doping of mobile fermions into the spin dimerized insulator such as spin Peierls state, valence bond glass, Heisenberg spins with next nearest neighbor exchange coupling and the Haldane gap state is discussed. The doping of fermions with narrow band into a Mott insulator with a spin gap results in the superconducting long range order in two- and three-dimensions, while results in the power law divergence of the pairing susceptibility with Tomonaga-Luttinger liquid character of charge in one-dimension. An example of numerical calculation in one-dimension is shown. The possible relevance of this mechanism to high-temperature superconductivity, where dynamical coupling of lattice distortion to spin may play a crucial role, is discussed. A relevant model Hamilto-nian with spin-phonon coupling and dynamical spin-Peierls fluctuation is proposed. © 1991, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Two dimensional coupled spin-fermion model as a model for high-Tc oxide is examined by using the perturbation method and the spin wave approximation in the weak Kondo coupling region. The logarithmic singularity appears in the fermion self energy. It is shown that one fermion doped into the Heisenberg spin system forms the self-trapped states of the fermion and spins. The doped many fermions remains localized as the self-trapped states below the critical fermion concentration. The relation to the Kondo effect is discussed. The relevance of our results to optical and photoemission experiments in high-Tc oxides is also discussed. © 1990, The Physical Society of Japan. All rights reserved.

The pairing susceptibility of the one-dimensional t-J model is examined numerically by the quantum transfer matrix method. The temperature dependence of the pairing susceptibility χs shows logarithmic behavior at low temperatures as χs~α log T for T being the temperature. The coefficient α is determined as a function of J/t and the fillingness for J and t being the exchange interaction and the transfer. Beyond that of noninteracting fermions, α grows rapidly with the increase of │J│. © 1990, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The spin wave theory of the two-dimensional Heisenberg antiferromagnet on a square lattice coupled with localized holes, i.e., extra spins, is investigated. This model is a limiting case of the coupled spin-fermion model presented recently to investigate the magnetic mechanism of high-Tc superconductivity. Two schemes of the spin wave theory are proposed according to the relative magnitude of JK (coupling between the extra and the substrate spins) to Js (coupling between the substrate spins). The following conclusions are obtained. (1) Small antiferromagnetic (AF) JK as well as ferromagnetic (F) JK enhances the AF long-range order suppressing the quantum fluctuations. Large AF JKi however, reduces the AF long-range order and enhances the quantum fluctuations. We obtain the large attractive interaction only in the latter case. (2) The susceptibility X± perpendicular to the staggered magnetization is logarithmically divergent with respect to the external frequency ω when one extra spin is introduced. © 1989, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

A coupled spin-fermion system is investigated as a model of high-Tc superconductivity. By the exact diagonalization technique, the binding energy of two fermions and several correlation functions in the ground state are calculated to study possible pairings of holes in orbitals of pπpσ d3z2-r2 etc. The bound states of fermions are suggested in two regions in the parameter space. In the small transfer region, it is caused by local defects induced in the antiferromagnet at the fermion sites. The larger transfer region is characterized by the relatively extended disturbance of the antifer-romagnetic correlation of the substrate spins, where the fermion forms singlet-like cloud around it. The latter is a characteristic feature of the antiferromagnetic fermion-spin coupling. The relevance of the latter region to high-Tc superconductivity is discussed. The possibilities of bound states of fermions in Kondo lattices are also investigated. © 1989, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Numerical results obtained from Monte Carlo simulation in the ground state and at finite temperatures as well as the exact diagonalization and the transfer matrix method are reported. Efficiency of the Monte Carlo method in the ground state is ex-amined. Spin, charge and superconducting correlations are investigated for the Hubbard and the t-J model in one and two dimensions. The momentum distribution in the one-dimensional Hubbard model shows fermi-liquid-like behavior at least in two orders of magnitude smaller energy scale than the band width. The short-range incommensurate spin correlation is observed and analyzed in the doped Hubbard and the t-J model both in one and two dimensions. In the ground state, the superconducting correlation shows the absence of system size dependence in two dimensions at the filling smaller than 0.8 and in one dimension at any filling. The binding energy of two fermions and the spin and charge distortion around an itinerant fermion are also discussed in the t-J and the coupled spin-fermion model. © 1989, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The possibility of chiral symmetry breaking in quantum spin systems is examined by the extrapolation of exactly diagonalized results on finite lattices in the ground state. Both on the triangular and the square lattice, linear dependence of squared chirality on the inverse linear size in the free boundary condition strongly suggests that the correlation of chirality defined by S1 (S2 × S2) is short-ranged in the thermodynamic limit, which also leads to the absence of the flux state. © 1989, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

A coupled spin-fermion model is presented as a two-band model of high-Tc superconductivity. The experimental relevance of the model is discussed. The high-Tc superconductivity is discussed the continuity of the strong coupling superconductivity to the weak coupling region. The attractive interaction of holes seems to exist over a wide range of parameters from weak to strong coupling cases. The small transfer region is useful to understand the pairing mechanism in the relevant strong coupling region. The model includes the effective Hamiltonian of the single-band Hubbard model as a special case. © 1988, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Quantum simulation results of superconducting correlations for strongly correlated electron systems are reported. An extended-type Hubbard model to take account of the role of oxygen sites in the CuO2 plane of high-Tc oxides is studied primarily. Superconducting susceptibility shows a tendency of quantitative enhancement at lower temperatures in contrast with the case of the single-band Hubbard model. It shows that a coupled two-band system, one with strong and the other with weak correlation, is favorable for superconductivity. A possible connection between superconducting and antiferromagnetic correlation is also discussed. © 1988, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

A hybrid algorithm for lattice fermions is examined. The fermion determinant is evaluated by a replacement of a matrix inversion with a stochastic iteration procedure. An advantage is that the computation time increases linearly with the increase of spatial system size. Efficiency and convergence in Hubbard-type models are investigated in various cases and temperatures. © 1988, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

A new hybrid-type algorithm is proposed for simulations of fermion lattices. The direct calculation of the matrix inversion operation is replaced with a stochastic iteration procedure. The computation time grows linearly with the increase of spatial system size. Applications to the Hubbard model on the 62, 122 and 162 square lattices are illustrated with no indication of enhancement for superconducting correlation in the non-half-filled band. © 1988, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Finite size calculation up to 18 spins combined with the extrapolation to the thermodynamic limit is performed to obtain thermodynamic properties of spin 1/2 triangular antiferromagnet. It shows that both of isotropic and Ising-like Heisenberg systems are in quantum spin fluid state at low temperatures with the singlet ground state. In contrast with the classical system, the result is consistent with the picture that the sublattice ordering has no relevance and no phase transition occurs. © 1987, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

A possible mechanism of superconductivity in oxide compounds is studied on the basis that hole carriers mainly occupy oxygen p-orbits. It is shown that oxygen holes may form singlet pairs with neighboring copper holes. It is proposed that mutually attractive interaction of the singlet pairs may lead to superconductivity. Results of quantum simulations show enhancement of pairing between two oxygen holes on a two-dimensional square lattice. © 1987, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The spin 1/2 triangular antiferromagnet with random exchange interaction is investigated using the finite size calculation. It is shown that the susceptibility diverges with a small randomness as T→0, where T is the temperature. The enhancement of the susceptibility by the randomness at low temperatures becomes larger when the Ising-like anisotropy of the exchange interaction increases. The possible connection of the divergent susceptibility to the spin glass-like order in the ground state is also pointed out. © 1987, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

A quantum transfer matrix method is proposed and examined. To obtain finite temperature properties, a small number of Monte Carlo samples for the trace summation is taken without the Monte Carlo sampling of the path integral. We introduce the method of a random orthonormal base in the Monte Carlo sampling. This makes it possible to investigate larger size systems than the exact diagonalization. An advantage of this method is that it does not have negative sign difficulty in the path integral as contrast to the usual quantum Monte Carlo method. A quantum molecular dynamics method is also proposed to investigate dynamical correlation functions. © 1986, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The competition between the charge-density-wave and singlet-superconducting phases is investigated for a strong-coupling quasi-one-dimensional system. For a half-filled band each phase appears separately, while for a quarter-filled band a coexistence region is found. © 1986 The American Physical Society.

Excited states in superconductors formed at normal impurities are investigated in the circumstance that the effective fermi energy is at most an order or magnitude larger than the superconducting gap and consequently the coherence length is roughly an order of magnitude larger than the lattice constant. It is discussed that the substantial spatial variation of the order parameter amplitude around an impurity easily occurs. The excitation energy of the bound state around the impurity extends down to a tenth of the gap in typical examples, which results in a new type of gapless-like behavior except at extremely low temperatures. The specific heat shows qualitatively different behavior from the BCS result and does not follow simple temperature dependence. © 1986, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Effects of randomness in the strong coupling electron systems, where the real space pairings of electrons have an important contribution are investigated in (quasi-) one-dimensional systems. For weak randomness, it is discussed that the nature of the ground state of purely one-dimensional systems does not necessarily reflect the low temperature properties of three-dimensional systems with quasi-one-dimensional anisotropy. In particular, the commensurate charge density wave and superconducting long range order persist for weak randomness. In the bipolaronic or biexcitonic region, Monte Carlo results show that the charge density wave is more strongly suppressed by randomness than superconductivity. The suppression of the CDW phase by impurities allows superconductivity to occur in parameter regime which were in a CDW phase for a pure system. © 1986, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Thermodynamic properties of non-relativistic quantum systems are treated by the Monte Carlo calculation of path integrals. This method can be applied to the N-body problem. For boson systems the importance sampling of permutation and coordinates is efficient. For fermion systems direct calculation of determinant of propagators is efficient to avoid the negative sign problem. © 1984, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Pressure-density and energy-density isotherms of 4He are obtained at temperatures higher than 4K and at densities lower than 0.05 mol/cm3 by applying path-integral Monte Carlo method to a system with Lennard-Jones 12-6 potential. Radial distribution function is also calculated. The results agree quantitatively with experimental data of 4He. © 1984, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

A spin polarized electron system is investigated by the recently developed technique for the Monte Carlo simulation of the path integral. It is found that the melting temperature of the Wigner crystal has the maximum value ~30 K at the density ~2.2 x 1012 cm-2. The phase diagram is obtained and the melting temperature shows monotonic decrease at the higher densities. The total energy shows hysteresis on the most part of the transition line. © 1984, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The higher order correction term is obtained for the Monte Carlo calculation of the path integral, The correction is expressed only by a modification of the potential term: V(r1,.,rN)®+V+(h+2/24m)(B/M)2 ENi=1(dV/dri)2, where ri's are coordinates of particles, N is number of particles with mass m, B is (kT)-l and M is number of partitions. By this method one can reduce the computation time remarkably. A rapid convergence of energy is obtained for the case of harmonic oscillator. © 1984, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The negative sign problem is a serious difficulty with most existing Monte Carlo methods of evaluating fermion systems of greater than one-dimension because it makes the computation of physical variables practically impossible. A simple and general averaging method is proposed for many-fermion systems. This method is completely free of the negative sign problem. The efficiency and convergence are verified in the Feynman's path integral calculations of a few simple models. © 1984, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The specific heat is calculated in the massive Thirring/quantum sine-Gordon limit on the one-dimensional XYZ model with the help of the Bethe ansatz approach. The Schottky-type anomaly appears asa contribution from the quantum soliton. The finite-temperature excitations are also discussed for these models. © 1983.

The thermodynamics of the anisotropic s-d model is formulated on the basis of the exact solution. The impurity part of the specific heat is calculated. © 1983.

Some results of the molecular dynamics simulation works are presented for the 4i4 chain. The Langevin equation was solved for various strengths of coupling to the heat bath. The central peak in the dynamic structure factor agrees rather well with the theoretical estimation. The importance of the nonlinear excitation is confirmed even in the presence of the random force and damping. © 1983, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Thermodynamics of the quantum sine-Gordon model is formulated in the presence of finite winding number. Several asymptotic cases are studied analytically. © 1983.

The thermodynamics of the quantum sine-Gordon model with finite winding numbers is investigated by the Bethe ansatz method. The temperature dependences of the specific heat and the winding number are calculated. The crossover from the case with the commensurate ground state to that with the incommensurate ground state is discussed. The quantum effect is shown to be significant in the thermodynamic properties of the system.

The thermodynamics of the massive Thirring model is discussed with the help of the Bethe Ansatz approach in a way different from Fowler and Zotos (1982). In particular a finite Debye cut-off is introduced to investigate effects of the lattice discreteness. The specific heat seems to have a structure as a sum of the Debye-type specific heat and a 'soliton' peak, when the authors take into account the relation of the massive Thirring model to the quantum sine-Gordon model. The finite temperature excitations are calculated. The excitation energy proposed by Fowler and Zotos is shown to have significance which is insensitive to the way of formulation.

The Bethe Ansatz approach is applied to calculate the specific heat of the massive-Thirring model with a Debye cutoff. Near the "classical" limit, the results are close to that of the classical sine-Gordon system. Specific heat is given by a super-position of Debye-type behavior and the "soliton" peak. © 1982.

Linear response of weakly coupled ϕ4 chains is investigated. The transfer integral method can be applied when the effect of the interchain coupling is taken into account using the mean field approximation. The Fokker-Planck equation is solved with a simple decoupling approximation for the phase space distribution function. We find a central peak structure in the dynamical structure factor. The intensity of the central peak diverges at the ferroelectric transition. This corresponds to the “softening” of the response of the domain wall. These phenomena may be observed in quasi-one-dimensional system such as CsD2PO4. © 1981, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

Linear response is investigated for the sine-Gordon chain. This is a direct application of a method introduced in a previous paper. The transfer integral method is applied. The Fokker-Planck equation is solved with a kind of decoupling approximation of the phase space distribution function. The frequency dependent mobility is obtained. It has a remarkable peak at a finite frequency and a small finite mobility at ω=0 for an appropriate choice of the damping constant. © 1981, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The linear response theory of the one dimensional nonlinear system, developed in I, is generalized to apply to a system with an arbitrary damping strength. In stead of the Smoluchowsky equation, the Fokker Planck equation is investigated. The transfer integral method is again applicable with a simple decoupling approximation. The dynamical structure factor for the φ4chain is found to be the sum of phonon peaks and a sharp central peak. As the damping strength reduces, the phonon peak becomes underdamped, while the structure of the cetatral peak is essentially the same as the strong damping case. The origin of the central peak is due to the response of the domain wall. © 1980, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

The linear response theory of the one dimensional nonlinear systems is formulated in the limit of the overdamping. Transfer integral method is applied to investigate the dynamical structure factor S (k =0, ω). The equation of motion for the distribution function is reduced to a set of independent equations for normal modes. As an example the structure factor for the φ4 chain is calculated to be the sum of a very narrow central peak and a broad overdamped phonon peak. The origin of the former is supposed to be the domain wall motion. © 1979, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

We consider the mechanism of the void lattice formation as a spinodal decomposition of vacancies. In the linear region of the spinodal decomposition, the void lattice constant is determined by estimating the periodicity growing in the spinodal decomposition. We assume that the void radius in the void lattice should be determined from the static stability according to Bullough and Stoneham et al. © 1978, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

A simple model is used to study the dependence of the sputtering yield on the incident atomic number (Z1). Scatterings between incident and target atoms are classified into two types, that is, large and small angle scatterings. Large angle scatterings are represented by random walks with a certain energy loss and small angle scatterings by another certain energy loss. The range distribution derived from this model is compared with other rigorous calculations. Sigmund's theory considerably overestimates the sputtering yield in the region where M2≫M1, M1 and M2 the mass of incident and target atoms respectively. Our simple model explains this as a surface boundary effect, i.e., as an effect due to escaping of energetic atoms from the surface. © 1978, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.

&lt;p&gt;量子多体系を記述する有効模型に対して基底状態及び低励起状態の波動関数を高精度に求める手法である多変数変分モンテカルロ法を，高効率かつ大規模並列に対応した汎用アプリケーション mVMC として公開を行った．本講演では，mVMCの利用方法とシミュレーション事例について報告を行う．&lt;/p&gt;

Topological aspects of matter have been extensively studied for materials with strong spin-orbit interaction, inspired by the seminal prediction of the topological insulator by Kane and Mele. Although the initial prediction ignored the electron correlation effects, the role of strong electron correlation in the topological properties of materials has been the subject of subsequent wide range of studies particularly for transition-metal as well as rare-earth compounds. The studies include those on the possibility of the topological insulators induced solely by the electron correlation effects. Among others, since the electron correlation and the spin orbit interaction compete, iridium oxides have been extensively studied. Sr_2IrO_4 isostructural to the copper oxide superconductors, R_2Ir_2O_7, which was predicted to show the Weyl semimetal and topological insulator characterized by the domain wall conduction in the magnetic ordered phase, and Na_2IrO_3 proposed as a candidate of Kitaev spin liquid are examples of hot topics for searching rich physics. We review recent studies on emergent phenomena and concepts generated by the interplay of spin-orbit interaction and electron correlation.

Layered 5d transition metal oxides (TMOs) have attracted significant interest
in recent years because of the rich physical properties induced by the
interplay between spin-orbit coupling, bandwidth and on-site Coulomb repulsion.
In Sr2IrO4, this interplay opens a gap near the Fermi energy and stabilizes a
Jeff=1/2 spin-orbital entangled insulating state at low temperatures. Whether
this metal-insulating transition (MIT) is Mott-type (electronic-correlation
driven) or Slater-type (magnetic-order driven) has been under intense debate.
We address this issue via spatially resolved imaging and spectroscopic studies
of the Sr2IrO4 surface using scanning tunneling microscopy/spectroscopy
(STM/S). The STS results clearly illustrate the opening of the (~150-250 meV)
insulating gap at low temperatures, in qualitative agreement with our
density-functional theory (DFT) calculations. More importantly, the measured
temperature dependence of the gap width coupled with our DFT+dynamical mean
field theory (DMFT) results strongly support the Slater-type MIT scenario in
Sr2IrO4. The STS data further reveal a pseudogap structure above the Neel
temperature, presumably related to the presence of antiferromagnetic
fluctuations.

{\it Ab initio} analyses of A$_2$IrO$_4$ (A=Sr, Ba) are presented. Effective<br />
Hubbard-type models for Ir 5$d$ $t_{2g}$ manifolds downfolded from the global<br />
band structure are solved based on the dynamical mean-field theory. The results<br />
for A=Sr and Ba correctly reproduce paramagnetic metals undergoing continuous<br />
transitions to insulators below the N\&#039;eel temperature $T_N$. These compounds<br />
are classified not into Mott insulators but into Slater insulators. However,<br />
the insulating gap opens by a synergy of the Neel order and significant band<br />
renormalization, which is also manifested by a 2D bad metallic behavior in the<br />
paramagnetic phase near the quantum criticality.

Apart from conventional phase transitions driven by thermal effects, quantum phase transitions generated by quantum fluctuations have their own mechanisms that are reflected in critical phenomena. Quantum phase transitions have an origin from spontaneous symmetry breaking commonly to thermal phase transitions. Even in this case, inherent quantum fluctuations substantially modify and yield new aspects. Quantum phase transitions have, however, another mechanism caused by topology changes, which gives completely new characters. Recently, a mechanism which connects these two has been found. Proximities from first-order transitions and phase separations as well as from multiphase coexistence also generate characteristic and unconventional quantum criticalities. Understanding novel quantum criticalities offers a firm basis of recent active researches on fields such as magnetism, ferroelectricity and metalinsulator transitions with potential applications and functional designs.

In a recent Comment [arXiv:0904.0454] on our Letter [Phys. Rev. Lett. 102,
056404 (2009); arXiv:0809:0950], Phillips criticizes one specific issue
discussed in our paper, concerning the spectral weight transfer, among our
wide-ranging clarifications of the filling-control Mott transition. Here we
show that all his criticisms have nothing to do with our contributions. Our
nontrivial finding on this particular aspect is a very quick, non-linear
increase in the spectral weight just above the chemical potential caused by
tiny doping to the Mott insulator, which is indeed unprecedented in the
literature. We call attention to its novelty in comparison with the
perturbation theory, and reemphasize our picture for the quick weight transfer,
that is, an avalanchine screening of doublon-holon binding energy.

We review attempts to reveal electronic structure of correlated electron systems based on first principles calculations. In particular transition metal oxides, rare earth compounds, organic conductors and nanoscale artificial structure are typical strongly correlated electron systems, and they are the target of our interest. In these classes of materials, newly discovered compounds and novel phenomena including not only magnetism, ferroelectricity and superconductivity but also unrevealed mysteries have opened a new avenue of research for condensed matter physics. They are the target for the present challenges for developing methods capable of treating electron correlation effects.

The terminology of &quot;first-principles calculation (FPC)&quot;, the subject of the present special issue, represents both methodology and basic principle for a research activity. The discipline is well known and the method has been developing in the condensed matter physics, so that FPC plays crucially important roles in a wide area of research. Nevertheless, we admit that it may not be totally obvious to those in other areas of physics what FPC means. With such a situation, we first explain the meaning of FPC, give a survey of its historical background and then explain the significance of each article included in this issue. The purpose of this article is to guide readers to understand the positioning of each article in FPC. We hope that this article may serve as a base camp for those who are not experts of FPC to visit the articles dealing with the cutting edge subjects of FPC.

We show that the phase boundary between the paramagnetic metal and the
nonmagnetic Mott insulator for the Hubbard model on a triangular lattice
obtained by Yoshioka et al. in arXiv:0811.1575 does not correctly represent
that of the thermodynamic limit but is an artifact of the 6 by 6 lattice they
rely on. After the system size extrapolation, the phase boundary is located at
U/t=5.2 as proposed by Morita et al., J. Phys. Soc. Jpn. 71 (2008) 2109 and in
contrast to Yoshioka et al. Here, U is the onsite Coulomb repulsion and t is
the nearest-neighbor transfer.

Correlated electrons often crystalize to the Mott insulator usually with some
magnetic orders, whereas the "quantum spin liquid" has been a long-sought
issue. We report numerical evidences that a nonmagnetic insulating (NMI) phase
gets stabilized near the Mott transition with remarkable properties:
The 2D Mott insulators on geometrically frustrated lattices contain a phase
with gapless spin excitations and degeneracy of the ground state in the whole
Brillouin zone of the total momentum. It has an interpretation for an
unexplored type of a quantum liquid. The present concept is useful in analyzing
a variety of experimental results in frustrated magnets including organic
BEDT-TTF compounds.

この論文は国立情報学研究所の電子図書館事業により電子化されました。

この論文は国立情報学研究所の電子図書館事業により電子化されました。

The ground-state properties of the two-dimensional Hubbard model with
nearest-neighbor and next-nearest-neighbor hoppings at half filling are studied
by the path-integral-renormalization-group method. The nonmagnetic-insulator
phase sandwiched by the the paramagnetic-metal phase and the
antiferromagnetic-insulator phase shows evidence against translational symmetry
breaking of the dimerized state, plaquette singlet state, staggered flux state,
and charge ordered state. These results support that the genuine Mott insulator
which cannot be adiabatically continued to the band insulator is realized
generically by Umklapp scattering through the effects of geometrical
frustration and quantum fluctuation in the two-dimensional system.

高温超伝導体に対するNMR、中性子散乱等の実験で観測されている擬ギャップ現象について、初期ベクトルをランダムサンプリングするランチョス法を用いて解析した。これは基底状態や低エネルギーの励起状態を数値的に厳密に求めるランチョス法と同じメモリーサイズで、有限温度の物理量を計算する手法である。この計算法の有効性について議論する。

Superconducting mechanism of cuprates is discussed in the light of the
proximity of the Mott insulator. The proximity accompanied by suppression of
coherence takes place in an inhomogeneous way in the momentum space in
finite-dimensional systems. Studies on instabilities of metals consisted of
such differentiated electrons in the momentum space are reviewed from a general
point of view. A typical example of the differentiation is found in the
flattening of the quasiparticle dispersion discovered around momenta $(\pi,0)$
and $(0,\pi)$ on 2D square lattices. This flattening even controls the
criticality of the metal-insulator transition. Such differentiation and
suppressed coherence subsequently cause an instability to the superconducting
state in the second order of the strong coupling expansion. The d-wave pairing
interaction is generated from such local but kinetic processes in the absence
of disturbance from the coherent single-particle excitations. The
superconducting mechanism emerges from a direct kinetic origin which is
conceptually different from the pairing mechanism mediated by bosonic
excitations as in magnetic, excitonic, and BCS mechanisms. Pseudogap phenomena
widely observed in the underdoped cuprates are then naturally understood from
the mode-mode coupling of d-wave superconducting (dSC) fluctuations repulsively
coupled with antiferromagnetic (AFM) ones. When we assume the existence of a
strong d-wave channel repulsively competing with AFM fluctuations under the
formation of flat and damped single-particle dispersion, we reproduce basic
properties of the pseudogap seen in the magnetic resonance, neutron scattering,
angle resolved photoemission and tunneling measurements in the cuprates.

高温超伝導体のアンダードープ領域での擬ギャップについて議論する。反強磁性(AFM)ゆらぎとd波超伝導(dSC)ゆらぎを、モード間カップリングを自己無撞着に扱って、スピン、dSCの相関長ζθ、ζdと1/(T_1T)を求める。その結果、AFMゆらぎの減衰γσがζdの増大とともに減少する場合、dSC短距離秩序の発達が、同時に増大するAFMゆらぎの低周波数成分を抑制する。そ結果1/T_&lt;2G&gt;が超伝導転移温度T_cまで増大する一方、1/T_1Tがより高温で減少に転じるAFMスピンの擬ギャップを再現した。γσがζdに依存しない場合、擬ギャップは消滅し、過剰ドープ領域での実験結果を再現する。

金属-絶縁体転移はバンド幅やキャリア濃度を変化させたときに, 量子力学的ゆらぎのために, 絶対零度で生じる相転移である. この中に, バンド絶縁体への転移, 乱れによるアンダーソン転移とならんで, 電子相関の効果が主役を演ずるモット絶縁体への転移がある. 強相関電子系は, 多くの量子力学的多体問題の中でも, 摂動論的手法を使いにくいなどの理由で, とりわけ理論上の難問を多く抱えている. モット絶縁体への転移はその最たるものである. この転移には, スピンや軌道の自由度が絶縁相と金属相で示す秩序とゆらぎの型に依存して, キャリア数が消滅する型, 有効質量が発散する型などの多様性がある. モット絶縁体近傍の金属は標準的な金属とかけ離れた性質を示すことが多い. 特に重要な性質として, バンド絶縁体への転移とは対照的に, コヒーレンスの抑制, 有効質量の増大など「悪い金属」としての特徴があり, 超伝導や磁気秩序, 電荷秩序, 軌道秩序などへの強い不安定性も伴う. 転移のきわで自由な電子の運動が異常に抑制されるさまと, その原因を記述する平均場理論とスケーリング理論を紹介しながら, 空間次元性の変化がもたらすこの転移の多様さと, 背後にある共通で単純な構造を解説する.

金属-絶縁体転移はバンド幅やキャリア濃度を変化させたときに, 量子力学的ゆらぎのために, 絶対零度で生じる相転移である. この中に, バンド絶縁体への転移, 乱れによるアンダーソン転移とならんで, 電子相関の効果が主役を演ずるモット絶縁体への転移がある. 強相関電子系は, 多くの量子力学的多体問題の中でも, 摂動論的手法を使いにくいなどの理由で, とりわけ理論上の難問を多く抱えている. モット絶縁体への転移はその最たるものである. この転移には, スピンや軌道の自由度が絶縁相と金属相で示す秩序とゆらぎの型に依存して, キャリア数が消滅する型, 有効質量が発散する型などの多様性がある. モット絶縁体近傍の金属は標準的な金属とかけ離れた性質を示すことが多い. 特に重要な性質として, バンド絶縁体への転移とは対照的に, コヒーレンスの抑制, 有効質量の増大など「悪い金属」としての特徴があり, 超伝導や磁気秩序, 電荷秩序, 軌道秩序などへの強い不安定性も伴う. 転移のきわで自由な電子の運動が異常に抑制されるさまと, その原因を記述する平均場理論とスケーリング理論を紹介しながら, 空間次元性の変化がもたらすこの転移の多様さと, 背後にある共通で単純な構造を解説する.

The dispersion relation of a doped hole in the half-filled 2D Hubbard model<br />
is shown to follow a k^4 law around the (0,pi) and (pi,0) points in the<br />
Brillouin zone. Upon addition of pair-hopping processes this dispersion<br />
relation is unstable towards a k^2 law. The above follows from T=0 Quantum<br />
Monte calculations of the single particle spectral function A(k, omega) on 16 X<br />
16 lattices. We discuss finite dopings and argue that the added term restores<br />
coherence to charge dynamics and drives the system towards a d_x^2 - y^2<br />
superconductor.

Quantum transitions between the Mott insulator and metals by controlling
filling in two-dimensional square lattice are characterized by a large
dynamical exponent $z=4$ where the origin of unusual metallic properties near
the Mott insulator are ascribed to the proximity of the transition. The scaling
near the transition indicates the formation of flat dispersion area due to
singular momentum dependence of the single-particle renormalization. The flat
dispersion controls critical properties of the Mott transition. An instability
of the flat dispersion to the d-wave superconducting order is discussed. We
also discuss a case of the Mott transition for a model of Mn perovskite
compounds with orbital degeneracy where orbital correlation length shows
critical divergence toward the metal-insulator transition.

この論文は国立情報学研究所の電子図書館事業により電子化されました。講義

We present high precision estimates of the exponents of a quantum phase
transition in a planar antiferromagnet. This has been made possible by the
recent development of cluster algorithms for quantum spin systems, the loop
algorithms. Our results support the conjecture that the quantum Heisenberg
antiferromagnet is in the same universality class as the O(3) nonlinear sigma
model. The Berry phase in the Heisenbrg antiferromagnet do not seem to be
relevant for the critical behavior.

高温超伝導のメカニズムのいろいろ、その比較とまとめ

最近脚光を浴びている数値計算による高温超電導の説明

バンド理論では説明できない強い相関を持った電子群をどう表すか

高温超電導で明らかになった異常な金属の正体

巷を賑わした高温超電導.その仕組みを解説する講座第1回目

「量子モンテカルロ法」とは何だろうか?多体量子系に対する数値計算の手法はいろいろあるが,そのうち「量子モンテカルロ法」は経路積分に基礎を置くものの総称である.経路積分が典型的な非摂動論的手法であることは知られている.ところで,物性物理学の研究の動向に目を向けてみると,強く相関する電子系の諸問題が困難な,しかし根本的な課題として広く認識されている.やや誇張していえば,強相関電子系の長い研究の歴史にもかかわらず,はっきりしたことは何も解明されていないというわけである.世に言う「高温超伝導」(すなわち銅酸化物超伝導体)の問題がその典型である.強相関電子系にアタックするのに適した非摂動論的手法として,「量子モンテカルロ法」の開発と応用が最近進んできた.まず開発途上のこの手法の現状に目を向けるのがこの解説の目的の一つである.強相関電子系の示す典型的な現象にモット転移(金属-絶縁体転移)がある.金属が絶縁体に転移するとき,電子の有効質量が発散するのか,それともキャリアの数がゼロになるのかという異なる二つの考え方がある.この対立概念を源として,金属-絶縁体転移に関する量子モンテカルロ計算の結果はより広範で基本的な問題提起へとつながってゆく.この問題を「量子モンテカルロ法」の応用例として考えてみるのが本稿のもう一つの目的である.

この論文は国立情報学研究所の電子図書館事業により電子化されました。

「量子モンテカルロ法」とは何だろうか?多体量子系に対する数値計算の手法はいろいろあるが,そのうち「量子モンテカルロ法」は経路積分に基礎を置くものの総称である.経路積分が典型的な非摂動論的手法であることは知られている.ところで,物性物理学の研究の動向に目を向けてみると,強く相関する電子系の諸問題が困難な,しかし根本的な課題として広く認識されている.やや誇張していえば,強相関電子系の長い研究の歴史にもかかわらず,はっきりしたことは何も解明されていないというわけである.世に言う「高温超伝導」(すなわち銅酸化物超伝導体)の問題がその典型である.強相関電子系にアタックするのに適した非摂動論的手法として,「量子モンテカルロ法」の開発と応用が最近進んできた.まず開発途上のこの手法の現状に目を向けるのがこの解説の目的の一つである.強相関電子系の示す典型的な現象にモット転移(金属-絶縁体転移)がある.金属が絶縁体に転移するとき,電子の有効質量が発散するのか,それともキャリアの数がゼロになるのかという異なる二つの考え方がある.この対立概念を源として,金属-絶縁体転移に関する量子モンテカルロ計算の結果はより広範で基本的な問題提起へとつながってゆく.この問題を「量子モンテカルロ法」の応用例として考えてみるのが本稿のもう一つの目的である.

この論文は国立情報学研究所の電子図書館事業により電子化されました。

実験室において実現可能な電子プラズマは, 密度や温度や次元の多様にひろがる領域のうちの一部分に限られている. 計算機シミュレーションを用いて, 「現状での実現可能性」という枠をとりはらい, 強結合プラズマの全体像を追究する試みが進みつつあるが, 量子系についてはまだはじまったばかりである. 一成分プラズマに対して行われたいくつかのシミュレーションを振り返って, 量子シミュレーションの方法と課題を紹介し, 状態図を含めて, 得られている結果を検討する.

この論文は国立情報学研究所の電子図書館事業により電子化されました。

この論文は国立情報学研究所の電子図書館事業により電子化されました。

この論文は国立情報学研究所の電子図書館事業により電子化されました。

この論文は国立情報学研究所の電子図書館事業により電子化されました。

ソリトンとは非線形系の局在した安定な励起に与えられた名である. 従ってソリトンは基本的には等速直線運動をするもので, その集団は理想気体に近いと想像される. この想像は正しいだろうか. このような非線形系の動的現象はどのように理解されているか. セントラルピークとソリトンの関係はどうか. サイン・ゴルドン系での拡散についての最近の論争などを述べる.

この論文は国立情報学研究所の電子図書館事業により電子化されました。