Ground state energies of the hubbard models and the hartree–fock approximation

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 [1] 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 show how to apply it to the system the hopping matrix of which has period greater than 1 (the case without strict translational invariance) — this allows us to consider systems the dispersion function of which is not (as assumed in [1]) a Morse function; (ii) we point out that the same technique allows to establish analogous estimates for a class of multiband Hubbard models.