# Localization and IDS Regularity in the Disordered Hubbard Model within Hartree-Fock Theory

## TL;DR

This paper demonstrates that weakly interacting fermions in a disordered Hubbard model exhibit localization at positive temperature, with exponential decay of eigenfunction correlators, and establishes H"older continuity of the density of states.

## Contribution

It applies the fractional moment method within Hartree-Fock theory to prove localization and regularity results in the disordered Hubbard model across different dimensions.

## Key findings

- Localization at positive temperature in the disordered Hubbard model
- Exponential decay of eigenfunction correlators in the regime of large disorder
- H"older continuity of the integrated density of states

## Abstract

Using the fractional moment method it is shown that, within the Hartree-Fock approximation for the Disordered Hubbard Hamiltonian, weakly interacting Fermions at positive temperature exhibit localization, suitably defined as exponential decay of eigenfunction correlators. Our result holds in any dimension in the regime of large disorder and at any disorder in the one dimensional case. As a consequence of our methods, we are able to show H\"older continuity of the integrated density of states with respect to energy, disorder and interaction using known techniques.