Topological number and Fermion Green's function of Strongly Interacting Topological Superconductors

It has been understood that short range interactions can reduce the classification of topological superconductors in all dimensions. In this paper we demonstrate by explicit calculations that when the topological phase transition between two distinct phases in the noninteracting limit is gapped out by interaction, the bulk fermion Green's function $G(i\omega)$ at the "transition" approaches zero as $G(i\omega) \sim \omega$ at certain momentum $\vec{k}$ in the Brillouin zone.