Beyond the Hubbard-I Solution with a One-Pole and a Two-Pole Self-Energy: Moment Approach

Details Beyond the Hubbard-I Solution with a One-Pole and a Two-Pole Self-Energy: Moment Approach Beyond the Hubbard-I Solution with a One-Pole and a Two-Pole Self-Energy: Moment Approach

1997-02-28

arxiv.org/abs/cond-mat/9703005v1

Physics

Condensed Matter

Strongly Correlated Electrons

Seven pages, 3 figures. Submitted to J. Phys.: Condens. Matter

Scientific paper

We have postulated a single pole for the self-energy looking for the consequences on the one-particle Green function, G(k,w), in the Hubbard model. We find that G(k,w) satisfies the first two sum rules or moments of Nolting (Z. Physik 225, 25 (1972)) for any values of the two unknown parameters of the self-energy. In order to find these two parameters we have used the third and four sum rules of Nolting. G(k,w) turns out to be identical to the one of Nolting which is beyond a Hubbard-I solution. Furthermore, we have also postulated a two-pole Ansatz for the self-energy which is equivalent to a three-pole ansatz for G(k,w). In the later case, we have fixed two of the frequencies. This Green function is also beyond the Hubbard-I solution. We present numerical results for the band structure and the spectral weights.

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