2 RIGOROUS THEOREMS ON THE MOMENTUM DISTRIBUTION-FUNCTIONS OF THE HUBBARD-MODEL AT HALF-FILLING

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