Dynamical mean-field theory and numerical renormalization group study of superconductivity in the attractive Hubbard model

TL;DR

This paper combines dynamical mean-field theory and numerical renormalization group methods to study superconductivity in the attractive Hubbard model, revealing deviations from mean-field predictions especially in strong coupling regimes.

Contribution

It extends the NRG method to handle self-consistent impurity models with superconducting symmetry breaking within DMFT, providing detailed insights into the BCS-BEC crossover.

Findings

Spectral weight shifts from quasiparticles to incoherent features in strong coupling.

Deviations from mean-field theory are significant in the BEC regime.

Charge fluctuations influence the single-particle spectra across the crossover.

Abstract

We present a study of the attractive Hubbard model based on the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG). For this study the NRG method is extended to deal with self-consistent solutions of effective impurity models with superconducting symmetry breaking. We give details of this extension and validate our calculations with DMFT results with antiferromagnetic ordering. We also present results for static and integrated quantities for different filling factors in the crossover from weak (BCS) to strong coupling (BEC) superfluidity. We study the evolution of the single-particle spectra throughout the crossover regime. Although the DMFT does not include the interaction of the fermions with the Goldstone mode, we find strong deviations from the mean-field theory in the intermediate and strong coupling (BEC) regimes. In particular, we show that low-energy charge fluctuations induce a transfer of spectral weight from the Bogoliubov quasiparticles to a higher-energy incoherent hump.