TWO-DIMENSIONAL ANDERSON-HUBBARD MODEL IN THE DMFT+ Σ APPROXIMATION
Kuchinskii E.Z., Kuleeva N.A., Nekrasov I.A., Sadovskii M.V.

Received: August 26, 2009

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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.