A numerical finite size scaling approach to many-body localization

TL;DR

This paper introduces a numerical method combining quantum Monte Carlo and finite size scaling to analyze many-body localization in disordered interacting electrons, revealing insulating behavior persists with interactions.

Contribution

The paper presents a novel numerical approach to study many-body localization using finite size scaling and quantum Monte Carlo simulations, extending understanding to interacting systems.

Findings

Localization properties are effectively extracted from Thouless conductance.

Interactions do not alter the universal beta(g) scaling function.

Systems remain insulating under weak to moderate interactions.

Abstract

We develop a numerical technique to study Anderson localization in interacting electronic systems. The ground state of the disordered system is calculated with quantum Monte-Carlo simulations while the localization properties are extracted from the ``Thouless conductance'' $g$, i.e. the curvature of the energy with respect to an Aharonov-Bohm flux. We apply our method to polarized electrons in a two dimensional system of size $L$. We recover the well known universal $\beta(g)=\rm{d}\log g/\rm{d}\log L$ one parameter scaling function without interaction. Upon switching on the interaction, we find that $\beta(g)$ is unchanged while the system flows toward the insulating limit. We conclude that polarized electrons in two dimensions stay in an insulating state in the presence of weak to moderate electron-electron correlations.