Exact diagonalization analysis of the Anderson-Hubbard model and comparison to real-space self-consistent Hartree-Fock solutions

TL;DR

This study computes exact ground states of the Anderson-Hubbard model on a 4x4 lattice, revealing strong charge screening effects and the effectiveness of Hartree-Fock approximations in reproducing local charge densities, suggesting new metallic states.

Contribution

It provides the first exact diagonalization analysis of the Anderson-Hubbard model on a 4x4 lattice and compares results with Hartree-Fock solutions, highlighting charge screening and metallic state mechanisms.

Findings

Strong charge homogeneity screening by Hubbard interaction

Hartree-Fock solutions accurately reproduce local charge densities

Evidence of dipolar backflow contributing to metallic states

Abstract

We have obtained the exact ground state wave functions of the Anderson-Hubbard model for different electron fillings on a 4x4 lattice with periodic boundary conditions - for 1/2 filling such ground states have roughly 166 million states. When compared to the uncorrelated ground states (Hubbard interaction set to zero) we have found strong evidence of the very effective screening of the charge homogeneities due to the Hubbard interaction. We have successfully modelled these local charge densities using a non-interacting model with a static screening of the impurity potentials. In addition, we have compared such wave functions to self-consistent real-space unrestricted Hartree-Fock solutions and have found that these approximate ground state wave functions are remarkably successful at reproducing the local charge densities, and may indicate the role of dipolar backflow in producing a novel metallic state in two dimensions.