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

TL;DR

This paper explores advanced self-energy models with one-pole and two-pole structures in the Hubbard model, deriving Green functions that satisfy key sum rules and extend beyond the Hubbard-I approximation, with numerical band structure results.

Contribution

It introduces a novel self-energy ansatz with one and two poles, satisfying multiple sum rules and providing Green functions beyond the Hubbard-I solution.

Findings

Green functions satisfy first two sum rules for any parameters

Two-pole self-energy yields a Green function beyond Hubbard-I

Numerical results show modified band structure and spectral weights

Abstract

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.