J. Stein, R. Oppermann: A spin-dependent Popov-Fedotov trick and a new loop expansion for the strong-coupling negative-U Hubbard model, Z. Phys. B 83 (1991) 333
We calculate fluctuation effects on Bose-condensation-type superconductivity in the strong-coupling negative-U Hubbard model by means of a new loop expansion. Our method is based on a spin-dependent modification of the Popov-Fedotov trick. We replace the Popov-Fedotov chemical potential by a fictitious imaginary magnetic field. This field is absorbed in spin-dependent semionic Matsubara frequencies, which allows for a mixed-statistics representation of the anisotropic quantum spin-1/2 Heisenberg model. We report results at one-loop order for the superconducting order parameter, for the critical temperature, for the chemical potential, and for the excitation spectra both above and below Tc. We identify mean-field results in zeroth loop order and we find both dimensional and filling (n-)depending singularities in interaction fluctuations at one-loop order. Renormalization of dimensional singularities is carried out in four dimensions. Divergencies with n(1-n) -> 0 in the dilute limits indicate the breakdown of mean-field solutions, but superconductivity persists for arbitrarily small n(1-n), if our loop expansion is interpreted by exponential behaviour as it is suggested by the abelian nonlinear sigma-model.