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arXiv · 2209.02361

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

Jacek Wojtkiewicz·Piotr H. Chankowski
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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.

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Jacek Wojtkiewicz, Piotr H. Chankowski. 2022-09-06. Ground state energies of the Hubbard models and the Hartree Fock approximation. https://arxiv.org/abs/2209.02361

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