Two Theorems on the Hubbard Model

Élliott H. Lieb

Élliott H. Lieb

Élliott H. Lieb

Sze-Shiang Feng

Guang-Shan Tian

In this article, based on a recent theorem by Lieb et al. (1968), we shall prove two theorems on the momentum distribution functions of the half-filled Hubbard model on a d-dimensional simple cubic lattice in a mathematically rigorous way. More precisely, we shall first show that the half-filled positive-U and negative-U Hubbard models have the same momentum distribution functions n up arrow (q) and n down arrow (q). Then, we will show that n sigma (q) are symmetric functions about the value n= 1/2 . Finally, we shall briefly discuss some possible applications of these theorems to the further numerical investigations on the ground state of the Hubbard model at half-filling.

Sze-Shiang Feng

Two theorems of the Hubbard model at nite temperature are proven employing the fluctuation–dissipation theorem and particle–hole transform. The main conclusion states that for the prototype Hubbard model, the expectation value of [Formula: see text] will be of order Nλ at any temperature except those critical.