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Solid State Communications

The symmetry of the momentum distribution functions in the Hubbard model at half-filling

Guang-Shan Tian

Published Oct 1, 1994• 1 citation
Publisher
DOI
10.1016/0038-1098(94)90891-5

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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.
The authors investigate the half-filled Hubbard model in one and two dimensions using approximations to the energy expressed as functionals of the momentum distribution. The functionals are calculated using the Hartree-Fock approximation and density functional theory in the local-spin-density and self-interaction-corrected (SIC) local-spin-density approximations (LSDA) by expressing the ground-state spin densities as a variational ansatz in which the momentum distribution enters as a variational quantity. The autthors calculate the momentum distribution, energy and local moment, as well as their ansatz orbitals, in all three approximations and find that the SIC always improves upon the LSDA.