Two-dimensional Anderson-Hubbard model in the DMFT + Σ approximation

The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular “bare” density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The “correlated metal,” Mott insulator, and correlated Anderson insulator phases are identified from the evolution of the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.     

Disorder and pseudogap in strongly correlated systems: Phase diagram in the DMFT + Σ approach

The influence of disorder and pseudogap fluctuations on the Mott insulator-metal transition in strongly correlated systems has been studied in the framework of the generalized dynamic mean field theory (DMFT + Σ approach). Using the results of investigations of the density of states (DOS) and optical conductivity, a phase diagram (disorder-Hubbard interaction-temperature) is constructed for the paramagnetic Anderson-Hubbard model, which allows both the effects of strong electron correlations and the influence of strong disorder to be considered. Strong correlations are described using the DMFT, while a strong disorder is described using a generalized self-consistent theory of localization. The DOS and optical conductivity of the paramagnetic Hubbard model have been studied in a pseudogap state caused by antiferromagnetic spin (or charge) short-range order fluctuations with a finite correlation length, which have been modeled by a static Gaussian random field. The effect of a pseudogap on the Mott insulator-metal transition has been studied. It is established that, in both cases, the static Gaussian random field (related to the disorder or pseudogap fluctuations) leads to suppression of the Mott transition, broadening of the coexistence region of the insulator and metal phases, and an increase in the critical temperature at which the coexistence region disappears.     

Correlated electrons in the presence of disorder

Several new aspects of the subtle interplay between electronic correlations and disorder are reviewed. First, the dynamical mean-field theory (DMFT) together with the geometrically averaged (“typical”) local density of states is employed to compute the ground state phase diagram of the Anderson-Hubbard model at half-filling. This non-perturbative approach is sensitive to Anderson localization on the one-particle level and hence can detect correlated metallic, Mott insulating and Anderson insulating phases and can also describe the competition between Anderson localization and antiferromagnetism. Second, we investigate the effect of binary alloy disorder on ferromagnetism in materials with f-electrons described by the periodic Anderson model. A drastic enhancement of the Curie temperature T_c caused by an increase of the local f-moments in the presence of disordered conduction electrons is discovered and explained.     

One-dimensional multiband correlated conductors and Anderson impurity physics

A single Anderson impurity model recently predicted, through its unstable fixed point, the phase diagram of a two-band model correlated conductor, well confirmed by dynamical mean-field theory in infinite dimensions. We study here the one-dimensional version of the same model and extract its phase diagram in the opposite limit of reduced dimensionality. As expected for one dimension, the Mott metal-insulator transition at half filling is replaced by a dimerized insulator-undimerized Mott insulator transition, while away from half filling the strongly correlated superconductivity for inverted Hund's rule exchange in infinite dimensions is replaced by dominant pairing fluctuations. Many other aspects of the one-dimensional system, in particular, the field theories and their symmetries, are remarkably the same as those of the Anderson impurity, whose importance appears enhanced.     

Mott-Hubbard transition versus Anderson localization in correlated electron systems with disorder

The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the geometrically averaged ("typical") local density of states. Correlated metal, Mott insulator, and Anderson insulator phases, as well as coexistence and crossover regimes, are identified. The Mott and Anderson insulators are found to be continuously connected.     

DMFT+Σ approach to disordered hubbard model

We briefly review the generalized dynamic mean-field theory DMFT+Σ applied to both repulsive and attractive disordered Hubbard models. We examine the general problem of metal–insulator transition and the phase diagram in the repulsive case, as well as the BCS–BEC crossover region of the attractive model, demonstrating a certain universality of single-electron properties under disordering in both models. We also discuss and compare the results for the density of states and dynamic conductivity in the repulsive and attractive cases and the generalized Anderson theorem behavior of the superconducting critical temperature in the disordered attractive case. A brief discussion of the behavior of Ginzburg–Landau coefficients under disordering in the BCS–BEC crossover region is also presented.     

Electronic structure calculations using dynamical mean field theory

The calculation of the electronic properties of materials is an important task of solid-state theory, albeit particularly difficult if electronic correlations are strong, e.g., in transition metals, their oxides and in f-electron systems. The standard approach to material calculations, the density functional theory in its local density approximation (LDA), incorporates electronic correlations only very rudimentarily and fails if the correlations are strong. Encouraged by the success of dynamical mean field theory (DMFT) in dealing with strongly correlated model Hamiltonians, physicists from the bandstructure and the many-body communities have joined forces and developed a combined LDA + DMFT method recently. Depending on the strength of electronic correlations, this new approach yields a weakly correlated metal as in the LDA, a strongly correlated metal or a Mott insulator. This approach is widely regarded as a breakthrough for electronic structure calculations of strongly correlated materials. We review this LDA + DMFT method and also discuss alternative approaches to employ DMFT in electronic structure calculations, e.g., by replacing the LDA part with the so-called GW approximation. Different methods to solve the DMFT equations are introduced with a focus on those that are suitable for realistic calculations with many orbitals. An overview of the successful application of LDA + DMFT to a wide variety of materials, ranging from Pu and Ce, to Fe and Ni, to numerous transition metal oxides, is given.     

Doping-driven orbital-selective Mott transition in multi-band Hubbard models with crystal field splitting

We have studied the doping-driven orbital-selective Mott transition in multi-band Hubbard models with equal band width in the presence of crystal field splitting. Crystal field splitting lifts one of the bands while leaving the others degenerate. We use single-site dynamical mean-field theory combined with continuous time quantum Monte Carlo impurity solver to calculate a phase diagram as a function of total electron filling N and crystal field splitting Δ. We find a large region of orbital-selective Mott phase in the phase diagram when the doping is large enough. Further analysis indicates that the large region of orbital-selective Mott phase is driven and stabilized by doping. Such models may account for the orbital-selective Mott transition in some doped realistic strongly correlated materials.     

Phase diagram of electron-hole systems: Interplay between exciton Mott transition and quantum pair condensation

Quasi-thermal-equilibrium states of electron-hole (e-h) systems in photoexcited insulators are studied from a theoretical viewpoint, stressing the exciton Bose-Einstein condensation (BEC), the e-h BCS-type pair-condensed state, and the exciton Mott transition between an insulating exciton/biexciton gas phase and a metallic e-h plasma phase. We determine the quasi-equilibrium phase diagram of the e-h system at zero and finite temperatures with applying the dynamical mean-field theory (DMFT) to the e-h Hubbard model with both repulsive and attractive on-site interactions. Effects of inter-site interactions on the exciton Mott transition are also clarified with applying the extended DMFT to the extended e-h Hubbard model.     

Quantum critical phase and Lifshitz transition in an extended periodic Anderson model

We study the quantum phase transition in f-electron systems as a quantum Lifshitz transition driven by selective-Mott localization in a realistic extended Anderson lattice model. Using dynamical mean-field theory (DMFT), we find that a quantum critical phase with anomalous ω/T scaling separates a heavy Landau-Fermi liquid from ordered phase(s). This non-Fermi liquid state arises from a lattice orthogonality catastrophe originating from orbital-selective Mott localization. Fermi surface reconstruction occurs via the interplay between and penetration of the Green function zeros to the poles, leading to violation of Luttinger's theorem in the strange metal. We show how this naturally leads to scale-invariant responses in transport. Thus, our work represents a specific DMFT realization of the hidden-FL and FL* theories, and holds promise for the study of 'strange' metal phases in quantum matter.     

Quantum Monte Carlo study of an interaction-driven band-insulator-to-metal transition

We study the transitions from band insulator to metal to Mott insulator in the ionic Hubbard model on a two-dimensional square lattice using determinant quantum Monte Carlo. Evaluation of the temperature dependence of the conductivity demonstrates that the metallic region extends for a finite range of interaction values. The Mott phase at strong coupling is accompanied by antiferromagnetic order. Inclusion of these intersite correlations changes the phase diagram qualitatively compared to dynamical mean field theory.     

Ten-fold spin-orbital degeneracy in the true d-electron Hubbard model of the Mott metal-insulator transition

The ten-fold spin-orbital degeneracy of true d-electrons is included in the non-spin-orbitally degenerate Hubbard model treatment theory of the Mott metal-insulator transition of Rice and Brinkman, and Gutzwiller. The Rice-Brinkman and Kohn phase diagrams of the Mott metal-insulator transition are shown to shift due to spin-orbital degeneracy of true d-electrons so as to increase the available phase space in the temperature-“interaction” Mott phase diagram for the formation of the antiferromagnetic insulator, superlattice metal or superlattice insulator states in these phase diagrams.     

Can correlations drive a band insulator metallic?

We analyze the effects of the on-site Coulomb repulsion U on a band insulator using dynamical mean field theory (DMFT). We find the surprising result that the gap is suppressed to zero at a critical Uc1 and remains zero within a metallic phase. At a larger Uc2 there is a second transition from the metal to a Mott insulator, in which the gap increases with increasing U. These results are qualitatively different from Hartree-Fock theory which gives a monotonically decreasing but nonzero insulating gap for all finite U.     

Correlated insulated phase suggests bond order between band and mott insulators in two dimensions

We investigate the ground state phase diagram of the half-filled repulsive Hubbard model in two dimensions in the presence of a staggered potential Delta, the so-called ionic Hubbard model, using cluster dynamical mean-field theory. We find that for large Coulomb repulsion, U > Delta, the system is a Mott insulator (MI). For weak to intermediate values of Delta, on decreasing U, the Mott gap closes at a critical value Uc1(Delta) beyond which a correlated insulating phase with possible bond order is found. Further, this phase undergoes a first-order transition to a band insulator (BI) at Uc2(Delta) with a finite charge gap at the transition. For large Delta, there is a direct first-order transition from a MI to a BI with a single metallic point at the phase boundary.     

Mott transition from a spin liquid to a Fermi liquid in the spin-frustrated organic conductor kappa-(ET)2Cu2(CN)3

The pressure-temperature phase diagram of the organic Mott insulator kappa-(ET)2Cu2(CN)3, a model system of the spin liquid on triangular lattice, has been investigated by 1H NMR and resistivity measurements. The spin-liquid phase is persistent before the Mott transition to the metal or superconducting phase under pressure. At the Mott transition, the spin fluctuations are rapidly suppressed and the Fermi-liquid features are observed in the temperature dependence of the spin-lattice relaxation rate and resistivity. The characteristic curvature of the Mott boundary in the phase diagram highlights a crucial effect of the spin frustration on the Mott transition.     

Commensurate-incommensurate transition of cold atoms in an optical lattice

An atomic gas subject to a commensurate periodic potential generated by an optical lattice undergoes a superfluid-Mott insulator transition. Confining a strongly interacting gas to one dimension generates an instability where an arbitrary weak potential is sufficient to pin the atoms into the Mott state; here, we derive the corresponding phase diagram. The commensurate pinned state may be detected via its finite excitation gap and the Bragg peaks in the static structure factor.     

Specific features of the electrical conductivity of V6O11

A study has been made of the electrical conductivity of V₆O₁₁ single crystals over a broad range of temperatures covering the regions of the metal phase, metal-insulator phase transition, and insulator phase. It has been shown that the electrical conductivity of the metal phase correlates with the Mott limit of minimum conductivity. To explain the temperature dependence of the electrical conductivity of the V₆O₁₁ insulator phase, the theory of hopping conduction taking into account the effect of thermal vibration of atoms on the resonance integral has been invoked.     

Mott transition, antiferromagnetism, and d-wave superconductivity in two-dimensional organic conductors

We study the Mott transition, antiferromagnetism, and superconductivity in layered organic conductors using the cellular dynamical mean-field theory for the frustrated Hubbard model. A d-wave superconducting phase appears between an antiferromagnetic insulator and a metal for t'/t=0.3-0.7 or between a nonmagnetic Mott insulator (spin liquid) and a metal for t'/t>or=0.8, in agreement with experiments on layered organic conductors including kappa-(ET)2Cu2(CN)3. These phases are separated by a strong first-order transition. The phase diagram gives much insight into the mechanism for -wave superconductivity. Two predictions are made.     

Cluster dynamical mean field theory of the Mott transition

We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge.