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

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 $\mathrm{\mid }U\mathrm{\mid }$, 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.