Delocalizing effect of the Hubbard repulsion for electrons on a two-dimensional disordered lattice

TL;DR

This study uses quantum Monte Carlo simulations to investigate how Hubbard repulsion influences electron localization in disordered two-dimensional lattices, revealing a strong delocalizing effect but leaving the metal-insulator transition unresolved.

Contribution

It provides the first detailed numerical analysis of the Hubbard model's impact on electron localization in disordered 2D systems using advanced quantum Monte Carlo methods.

Findings

Hubbard repulsion strongly delocalizes electrons in disordered 2D lattices.

Numerical limitations prevent definitive conclusions about a metal-insulator transition.

Charge density differences reveal localization properties of added particles.

Abstract

We study numerically the ground-state properties of the repulsive Hubbard model for spin-1/2 electrons on two-dimensional lattices with disordered on-site energies. The projector quantum Monte Carlo method is used to obtain very accurate values of the ground-state charge density distributions with $N_p$ and $N_p+1$ particles. The difference in these charge densities allows us to study the localization properties of an added particle. The results obtained at quarter-filling on finite clusters show that the Hubbard repulsion has a strong delocalizing effect on the electrons in disordered 2D lattices. However, numerical restrictions do not allow us to reach a definite conclusion about the existence of a metal-insulator transition in the thermodynamic limit in two-dimensions.