A spin-dependent Popov-Fedotov trick and a new loop expansion for the strong coupling negativeU Hubbard model

Abstract

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 spindependent 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 α, for the critical temperature, for the chemical potential, and for the excitation spectra both above and belowT _c. We identify mean field results in zeroth loop order and we find both dimensional and filling (v-)depending singularities in interaction fluctuations at one loop order. Renormalization of dimensional singularities is carried out in 4 dimensions. Divergencies withv (1−v)→0 in the dilute limits indicate the breakdown of mean field solutions, but superconductivity persists for arbitrarily smallv(1−v) if our loop expansion is interpreted by exponential behaviour as it is suggested by the abelian nonlinear sigma model.