Application of Many-body Non-perturbative Theories to the Three-Dimensional Attractive Hubbard Model

TL;DR

This paper evaluates various many-body theories applied to the 3D attractive Hubbard model, comparing their accuracy with quantum Monte Carlo simulations and proposing a method to identify the pseudogap onset temperature.

Contribution

It systematically compares GW methods with DQMC in the 3D attractive Hubbard model and introduces a new approach to determine the pseudogap temperature.

Findings

GW methods are reliable in weak to intermediate coupling regimes.

Post-GW improves Green's functions and density of states in the superconducting phase.

Critical exponents match well with the 3D XY model.

Abstract

The attractive Fermi-Hubbard model stands out as a simple model for studying the pairing and superconductivity of fermions on a lattice. In this article, we apply several many-body theories in the three-dimensional attractive Hubbard model. Specifically, we compare the results of various GW methods with DQMC simulations and observe that they provide reliable results in the weak to intermediate coupling regime. The critical exponents also agree well with the accurate results obtained from the 3D XY model. In the superconducting phase, the post-GW method significantly improves the description of Green's functions and density of states. Additionally, we propose a method to determine the temperature at which the pseudogap appears.