Gutzwiller variational theory for the Hubbard model with attractive interaction

TL;DR

This paper applies a Gutzwiller variational approach to the negative-U Hubbard model, revealing notable differences from standard BCS theory, especially in the superconducting gap, and provides analytical results for small interaction strengths.

Contribution

It introduces a Gutzwiller variational method for the negative-U Hubbard model, offering new insights into its superconducting properties beyond standard BCS theory.

Findings

Significant differences in superconducting gap compared to BCS theory

Analytical expressions for order parameter and gap at small |U|

Comparison with perturbation theory results

Abstract

We investigate the electronic and superconducting properties of a negative-U Hubbard model. For this purpose we evaluate a recently introduced variational theory based on Gutzwiller-correlated BCS wave functions. We find significant differences between our approach and standard BCS theory, especially for the superconducting gap. For small values of $|U|$, we derive analytical expressions for the order parameter and the superconducting gap which we compare to exact results from perturbation theory.