Topological number and fermion Green's function for strongly interacting topological superconductors

Abstract

It has been understood that short range interactions can reduce the classification of topological superconductors in all dimensions. In this Rapid Communication 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 $G(i\ensuremath{\omega})$ at the ``transition'' approaches zero as $G(i\ensuremath{\omega})\ensuremath{\sim}\ensuremath{\omega}$ at certain momentum $\stackrel{P\vec}{k}$ in the Brillouin zone.