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.

根据“民间知识”，应用于 Hubbard 模型的 Hartree-Fock (HF) 近似在小耦合U的极限下变得精确（| U|越小，HF 近似越好）。在[ 1 ]中，巴赫和波尔乔通过对最简单版本的哈伯德模型的真实基态能量与该量的 HF 近似值之间的差异进行严格估计，证实了这一断言的某个版本。在本文中，我们将他们的结果扩展到两个方向：（i）我们展示了如何将其应用于跳频矩阵周期大于 1 的系统（没有严格平移不变性的情况）——这使我们能够考虑系统的色散其函数不是（如[ 1 ]中假设的）莫尔斯函数；(ii) 我们指出，相同的技术允许为一类多频带哈伯德模型建立类似的估计。