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Physical review. B, Condensed matter

Metallic state of the Hubbard model with randomly distributed Coulomb interactions

Tetsuya Mutou

Published Jul 15, 1999• 7 citations
Publisher

Abstract

We study the inhomogeneous Hubbard model with randomly distributed impurity sites with Coulomb interactions embedded in noninteracting host sites, using the dynamical mean-field theory extended to the case with site-dependent Coulomb interactions. Comparison is made with the Hubbard model which possesses the averaged effective Coulomb interactions which are proportional to impurity concentrations. For high concentrations, such a picture with the averaged effective Coulomb interactions gives reasonable results for some quantities, such as the density of states at low temperatures. At high temperatures, however, components of impurity sites and host sites are separated, leading to a clear difference from those in the homogeneous case. On the other hand, for lower concentrations, the difference appears even at low temperatures. Impurity concentration dependences of the coefficient of the specific heat linear in T and the coefficient of the resistivity square in T are different from those of the homogeneous one with the effective Coulomb interactions. In the inhomogeneous system, the high-concentration regime described by the Fermi liquid is continuously connected to the low-concentration regime which may be described by the ensemble of Kondo impurities.

DOI
10.1103/physrevb.60.2268

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We study the inhomogeneous Hubbard model with randomly distributed impurity sites with Coulomb interactions embedded in noninteracting host sites, using the dynamical mean-field theory extended to the case with site-dependent Coulomb interactions. Comparison is made with the Hubbard model which possesses the averaged effective Coulomb interactions which are proportional to impurity concentrations. For high concentrations, such a picture with the averaged effective Coulomb interactions gives reasonable results for some quantities, such as the density of states at low temperatures. At high temperatures, however, components of impurity sites and host sites are separated, leading to a clear difference from those in the homogeneous case. On the other hand, for lower concentrations, the difference appears even at low temperatures. Impurity concentration dependences of the coefficient of the specific heat linear in T and the coefficient of the resistivity square in T are different from those of the homogeneous one with the effective Coulomb interactions. In the inhomogeneous system, the high-concentration regime described by the Fermi liquid is continuously connected to the low-concentration regime which may be described by the ensemble of Kondo impurities.
We explore the two-dimensional extended Hubbard model on the triangular lattice in the high doping regime. On-site and nearest-neighbour repulsive interactions are treated in a non-perturbative way by means of Extended Dynamical Mean Field Theory. We compute the low-temperature phase diagram, displaying a metallic phase and a symmetry-broken phase for strong intersite repulsions. We describe the correlation effects on both single-particle and two-particle observables in the metallic phase. Whereas single-particle spectra feature a Hubbard satellite typical of strongly correlated systems, local susceptibilities remain close to their non-interacting limit, even for large on-site repulsions. We argue that this behaviour is typical of the strongly doped case. We also report a region in parameter space with negative static local screening.
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Abstract We consider Anderson localization in the half-filled Anderson–Hubbard model in the presence of either random on-site interactions or spatially alternating interactions in the lattice. By using dynamical mean field theory with the equation of motion method as an impurity solver, we calculate the arithmetically and geometrically averaged local density of states and derive the equations determining the critical value for the phase transition between metallic, Anderson and Mott insulating phases. The nonmagnetic ground state phase diagrams are constructed numerically. We figure out that the presence of Coulomb disorder drives the system toward the Anderson localized phase that can occur even in the absence of Anderson structural disorder. For the spatially alternating interactions, we find that the metallic region is reduced and the Anderson insulator one is enlarged with increasing interaction modulation. Our obtained results are relevant to current research in ultracold atoms in disordered optical lattices where metal–insulator transition can be observed experimentally by using ultracold atom techniques.
We find marginal-Fermi-liquid- (MFL) like behavior in the Hubbard model on a square lattice for a range of hole doping and on-site interaction parameter U. Thereby we use a self-consistent projection operator method. It enables us to compute the momentum and frequency dependence of the single-particle excitations with high resolution. The Fermi surface is found to be holelike in the underdoped regime and electronlike in the overdoped regime. Our calculations concern normal state properties of the system. When a comparison is possible, we find consistency with finite temperature quantum Monte Carlo results. We also find a discontinuous change with doping concentration from a MFL to a Fermi-liquid behavior resulting from a collapse of the lower Hubbard band. This renders Luttinger's theorem inapplicable in the underdoped regime.
In this thesis, we study quantum impurity models by means of the diagrammatic perturbation theory. First, parquet equations are simplified in the strong coupling regime and low temperatures and an analytically controllable approximation results. We apply it to both the single impurity Anderson model and the Hubbard model in the dynamical mean-field approximation and we study properties of the solution. We recover the correct three-peak density of states including the Kondo resonance and prove that it has the correct exponential scaling with increasing interaction strength. Our approximate scheme is further extended to multi-orbital models. We explicitly solve the two-orbital single impurity Anderson model and the Hubbard model and calculate effects of the Hund exchange interaction and the crystal field.