Ground state energies of the Hubbard models and the Hartree Fock approximation

TL;DR

This paper rigorously analyzes the accuracy of the Hartree-Fock approximation for Hubbard models, extending previous results to more general cases including non-translationally invariant systems and multiband models.

Contribution

It extends prior rigorous estimates of the Hartree-Fock approximation's accuracy to models with less symmetry and to multiband Hubbard models.

Findings

Provides bounds on the difference between true and Hartree-Fock ground-state energies.

Extends rigorous estimates to non-translationally invariant Hubbard models.

Applies analysis to a class of multiband Hubbard models.

Abstract

According to the `folk knowledge', the Hartree-Fock (H-F) approximation applied to the Hubbard model becomes exact in the limit of small coupling $U$ (the smaller $|U|$, the better is the H-F approximation). In \cite{BP} Bach and Poelchau have substantiated a certain version of this assertion by providing a rigorous estimate of the difference between the true ground-state energy of the simplest version of the Hubbard model and the H-F approximation to this quantity. In this paper we extend their result in two directions: i) we relax the assumption about the strict translational invariance of the hopping matrix, ii) we prove an analogous estimate for a class of multiband Hubbard models.