Two-dimensional Anderson-Hubbard model in DMFT+Sigma approximation

TL;DR

This paper investigates the phase diagram and electronic properties of the two-dimensional Anderson-Hubbard model using DMFT+Sigma, revealing the coexistence of Mott and Anderson insulator phases and identifying a finite-size Anderson transition.

Contribution

It extends the DMFT+Sigma approach to analyze the combined effects of strong correlations and disorder in 2D systems, providing a comprehensive phase diagram.

Findings

Identified phases: correlated metal, Mott insulator, Anderson insulator.

Demonstrated coexistence of Mott-Hubbard and Anderson metal-insulator transitions.

Localization length is nearly unaffected by Hubbard interaction strength.

Abstract

Density of states, dynamic (optical) conductivity and phase diagram of paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean-field theory (DMFT+Sigma approximation). Strong correlations are accounted by 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). Phases of "correlated metal", Mott insulator and correlated Anderson insulator are identified from the evolution of density of states, optical conductivity and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of the finite size, allowing us to construct the complete zero-temperature phase diagram of paramagnetic Anderson-Hubbard model. Localization length in our approximation is practically independent of the strength of Hubbard correlations. However, the divergence of localization length in finite size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.