Self-consistent study of Anderson localization in the Anderson-Hubbard model in two and three dimensions

TL;DR

This paper investigates how electron-electron interactions influence Anderson localization in the Anderson-Hubbard model across two and three dimensions, revealing complex behaviors including nonmonotonic localization length and interaction-induced phases.

Contribution

It introduces a self-consistent approach combining Mott-Hubbard physics and static screening to analyze localization, uncovering new interaction-driven phenomena in disordered systems.

Findings

Localization length shows nonmonotonic behavior in 2D.

Interaction enhances localization length exponentially at intermediate disorder.

In 3D, a Mott-Hubbard-assisted localized phase exists between metal and insulator.

Abstract

We consider the change in electron localization due to the presence of electron-electron repulsion in the \HA model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. We find rich nonmonotonic behavior of the localization length $\xi$ in two-dimensional systems, including an interaction-induced exponential enhancement of $\xi$ for small and intermediate disorders although $\xi$ remains finite. In three dimensions we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbard-gapped phases. For small $U$ there is re-entrant behavior from the Anderson localized phase to the metallic phase.