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Solid State Communications

On the hubbard model at half filling

David Djajaputra, J. Ruvalds

Published Nov 1, 1998• 2 citations
Publisher
DOI
10.1016/s0038-1098(98)00487-6

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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.
Numerical simulations on the half-filled 3-D Hubbard model clearly show the onset of Néel order. Simulations of the 2-D electron-phonon Holstein model show the competition between the formation of a Peierls-CDW state and a superconducting state. However, the behavior of the partly filled 2-D Hubbard model is more difficult to determine. At half-filling, the anti-ferromagnetic correlations grow as T is reduced. Doping away from half-filling supresses these correlations, and we find that there is a weak attractive pairing interaction in the d -wave channel. However, the strength of the pair field susceptibility is weak at the temperatures and lattice sizes we have simulated, and the nature of the low-temperature state of the nearly half-filled Hubbard model remains open.