One-Electron Spectral Functions of the Attractive Hubbard Model for Intermediate Coupling

We calculate the one-electron spectral function of the attractive (negative-$U$) Hubbard model. We work in the intermediate coupling and low density regime and obtain the self-energy in an approximate analytical form. The excitation spectrum is found to consist of three branches. The results are obtained in a framework, based on the self-consistent T-matrix approximation, which is compatible with the Mermin-Wagner theorem.