Abstract
We study the $T=0$ crossover from the BCS superconductivity to Bose-Einstein condensation in the attractive Hubbard Model within dynamical mean field theory (DMFT) in order to examine the validity of Hartree-Fock-Bogoliubov (HFB) mean field theory, usually used to describe this crossover, and to explore the physics beyond it. Quantum fluctuations are incorporated using iterated perturbation theory as the DMFT impurity solver. We find that these fluctuations lead to large quantitative effects in the intermediate coupling regime, leading to a reduction of both the superconducting order parameter and the energy gap relative to the HFB results. A qualitative change is found in the single-electron spectral function, which now shows an incoherent spectral weight for energies larger than three times the gap, in addition to the usual Bogoliubov quasiparticle peaks.
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