Variational Monte Carlo Study of Anderson Localization in the Hubbard Model

TL;DR

This study investigates how electron interactions influence Anderson localization in the Hubbard model using variational Monte Carlo methods, revealing that strong correlations can screen disorder and increase localization length despite reduced persistent currents.

Contribution

It introduces a variational Gutzwiller ansatz to analyze the interplay of interactions and disorder in the Hubbard model, providing new insights into localization near the Mott transition.

Findings

Persistent current decreases with strong correlations at half filling.

Disorder potential is strongly screened at large interaction strength.

Localization length increases with interaction strength despite current suppression.

Abstract

We have studied the effects of interactions on persistent currents in half-filled and quarter-filled Hubbard models with weak and intermediate strength disorder. Calculations are performed using a variational Gutzwiller ansatz that describes short range correlations near the Mott transition. We apply an Aharonov-Bohm magnetic flux, which generates a persistent current that can be related to the Thouless conductance. The magnitude of the current depends on both the strength of the screened disorder potential and the strength of electron-electron correlations, and the Anderson localization length can be extracted from the scaling of the current with system size. At half filling, the persistent current is reduced by strong correlations when the interaction strength is large. Surprisingly, we find that the disorder potential is strongly screened in the large interaction limit, so that the localization length grows with increasing interaction strength even as the magnitude of the current is suppressed. This supports earlier dynamical mean field theory predictions that the elastic scattering rate is suppressed near the Mott transition.