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Physical Review B

Statistics of local density of states in the Falicov-Kimball model with local disorder

Minh-Tien Tran

Published Dec 26, 2007• 13 citations
Publisher

Abstract

Statistics of the local density of states in the two-dimensional Falicov-Kimball model with local disorder is studied by employing the statistical dynamical mean-field theory. Within the theory, the local density of states and its distributions are calculated through stochastic self-consistent equations. The most probable value of the local density of states is used to monitor the metal-insulator transition driven by correlation and disorder. Nonvanishing of the most probable value of the local density of states at the Fermi energy indicates the existence of extended states in the two-dimensional disordered interacting system. It is also found that the most probable value of the local density of states exhibits a discontinuity when the system crosses from extended states to the Anderson localization. A phase diagram is also presented.

DOI
10.1103/physrevb.76.245122

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Statistics of the local density of states in the two-dimensional Falicov-Kimball model with local disorder is studied by employing the statistical dynamical mean-field theory. Within the theory, the local density of states and its distributions are calculated through stochastic self-consistent equations. The most probable value of the local density of states is used to monitor the metal-insulator transition driven by correlation and disorder. Nonvanishing of the most probable value of the local density of states at the Fermi energy indicates the existence of extended states in the two-dimensional disordered interacting system. It is also found that the most probable value of the local density of states exhibits a discontinuity when the system crosses from extended states to the Anderson localization. A phase diagram is also presented.
Statistics of the local density of states in the two-dimensional Falicov-Kimball model with local disorder is studied by employing the statistical dynamical mean-field theory. Within the theory the local density of states and its distributions are calculated through stochastic self-consistent equations. The most probable value of the local density of states is used to monitor the metal-insulator transition driven by correlation and disorder. Nonvanishing of the most probable value of the local density of states at the Fermi energy indicates the existence of extended states in the two-dimensional disordered interacting system. It is also found that the most probable value of the local density of states exhibits a discontinuity when the system crosses from extended states to the Anderson localization. A phase diagram is also presented.
The statistical dynamical mean field theory is used to study the metal-insulator transition in the two-dimensional Falicov-Kimball model with local disorder. Within the theory, the local density of states and its distributions are calculated. As a measure of the metal-insulator transition driven by correlation and disorder, the most probable value of the local density of states is determined. The most probable value of the local density of states is found to exhibit a discontinuity when the system crosses from extended states to localization. A phase diagram is also presented.
The ground-state phase diagrams of the Falicov-Kimball model with local disorder are derived within the dynamical mean-field theory and using the geometrically averaged (``typical'') local density of states. Correlated metal, Mott insulator, and Anderson insulator phases are identified. The metal-insulator transitions are found to be continuous. The interaction and disorder compete with each other stabilizing the metallic phase against the occurring one of the insulators. The Mott and Anderson insulators are found to be continuously connected.
Strongly correlated electrons with box disorder in high-dimensional lattices are investigated. We apply a statistical dynamical mean-field theory that treats local correlations nonperturbatively. The incorporation of a finite lattice connectivity allows for the detection of disorder-induced localization via the probability distribution function of the local density of states. We obtain a complete paramagnetic ground-state phase diagram and find correlation-induced as well as disorder-induced metal-insulator transitions. Our results qualitatively confirm predictions obtained by typical medium theory. Moreover, we find that the probability distribution function of the local density of states in the metallic phase strongly deviates from a log-normal distribution as found for the noninteracting case.
The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the H\"older mean local density of states. A critical disorder strength is determined in the Anderson-Falicov-Kimball model, and the arithmetic and the geometric averages are found to be just particular means used, respectively, to detect or not the Anderson localization. Correlated metal, Mott insulator, and Anderson insulator phases, as well as coexistence and crossover regimes, are analyzed in this perspective.
Strongly correlated fermions in a crystal or in an optical lattice in the presence of binary-alloy disorder are investigated. We employ the statistical dynamical mean-field theory, which incorporates both fluctuations due to disorder and local correlations due to interaction, to solve the Anderson-Hubbard model. Localization due to disorder is studied by means of the probability distribution function of the local density of states. We obtain a complete paramagnetic ground state phase diagram consisting of disordered correlated metal, Anderson-Mott insulator, and band insulator.