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

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.

17 pages, 12 figures; (with amendments in section VI)

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• Repulsive vs. attractive Hubbard model: transport properties and spin-lattice relaxation rate
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• Disorder Effects in BCS-BEC Crossover Region of Attractive Hubbard Model
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• Ginzburg - Landau Expansion in BCS - BEC Crossover Region of Disordered Attractive Hubbard Model
• Embedding Dynamical Mean-Field Theory for Superconductivity in Layered Materials and Heterostructures
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