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arXiv:1002.3696 · International Journal of Modern Physics B

ANDERSON LOCALIZATION VS. MOTT–HUBBARD METAL–INSULATOR TRANSITION IN DISORDERED, INTERACTING LATTICE FERMION SYSTEMS

Krzysztof Byczuk, Walter Hofstetter, D. Vollhardt

Published May 20, 2010• 51 citations
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Abstract

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.

DOI
10.1142/s0217979210064575

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Dynamical mean-field theory (DMFT) is a successful method to investigate interacting lattice fermions. In these lecture notes we present an introduction into the DMFT for lattice fermions with interaction, disorder and external inhomogeneous potentials. This formulation is applicable to electrons in solids and to cold fermionic atoms in optical lattices. We review here our investigations of the Mott-Hubbard and Anderson metal-insulator transitions in correlated, disordered systems by presenting selected surprising results. 1.

•Jun 1, 2008•1 citation
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 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.
The magnetic ground state phase diagram of the disordered Hubbard model at half-filling is computed in dynamical mean-field theory supplemented with the spin resolved, typical local density of states. The competition between many-body correlations and disorder is found to stabilize paramagnetic and antiferromagnetic metallic phases at weak interactions. Strong disorder leads to Anderson localization of the electrons and suppresses the antiferromagnetic long-range order. Slater and Heisenberg antiferromagnets respond characteristically differently to disorder. The results can be tested with cold fermionic atoms loaded into optical lattices.
The interplay between disorder acting only on particles with a given spin projection (spin-dependent disorder) and antiferromagnetic long-range order is explored. To this end the magnetic ground state phase diagram of the Hubbard model at half-filling is computed within dynamical mean-field theory combined with the geometric average over disorder, a method sensitive to Anderson localization. Four distinct phases are identified: a paramagnetic metal, an antiferromagnetic insulator, and two types of spin-selective localized phases. The phase diagram may be tested experimentally using cold fermions in optical lattices subject to spin-dependent random potentials.
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.
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.
Dynamical mean-field theory (DMFT) is a successful method to investigate interacting lattice fermions. In these lecture notes we present an introduction into the DMFT for lattice fermions with interaction, disorder and external inhomogeneous potentials. This formulation is applicable to electrons in solids and to cold fermionic atoms in optical lattices. We review here our investigations of the Mott-Hubbard and Anderson metal-insulator transitions in correlated, disordered systems by presenting selected surprising results. 1.