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arXiv:0911.0934 · Physical Review B

Mott-Hubbard and Anderson metal-insulator transitions in correlated lattice fermions with binary disorder

D. Semmler, Krzysztof Byczuk, Walter Hofstetter

Published Mar 5, 2010• 36 citations
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Abstract

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.

DOI
10.1103/physrevb.81.115111

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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.
We review recent progress in our theoretical understanding of strongly correlated fermion systems in the presence of disorder. Results were obtained by the application of a powerful nonperturbative approach, the dynamical mean-field theory (DMFT), to interacting disordered lattice fermions. In particular, we demonstrate that DMFT combined with geometric averaging over disorder can capture Anderson localization and Mott insulating phases on the level of one-particle correlation functions. Results are presented for the ground state phase diagram of the Anderson–Hubbard model at half-filling, both in the paramagnetic phase and in the presence of antiferromagnetic order. We find a new antiferromagnetic metal which is stabilized by disorder. Possible realizations of these quantum phases with ultracold fermions in optical lattices are discussed.
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.
Strongly correlated fermions in three- and two-dimensional optical lattices with experimentally realistic speckle disorder are investigated. We extend and apply the statistical dynamical mean-field theory, which treats local correlations nonperturbatively, to incorporate on-site and hopping-type randomness on equal footing. Localization due to disorder is detected via the probability distribution function of the local density of states. We obtain a complete paramagnetic ground state phase diagram for experimentally realistic parameters and find a strong suppression of the correlation-induced metal insulator transition due to disorder. Our results indicate that the Anderson-Mott and the Mott insulator are not continuously connected due to the specific character of speckle disorder. Furthermore, we discuss the effect of finite temperature on the single-particle spectral function.
The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition.
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.