Detect topological quantum phases in a one-dimensional interactional fermion system

Abstract

Based on the Su-Schriefferheeger (SSH) and Kitaev hybrid fermion model, we study the Berry phase in detecting different types of topological phases. We find that, under the twist boundary condition, the low energy spectra play remarkable roles in determining the Berry phase value. The non-zero Berry phase combined with the low energy spectra can be used to distinguish different types of topological quantum states. Furthermore, we consider the influence of interactions on the system. Through analysis of the Berry phase, the entanglement entropy, and the electron occupation, a new quantum phase is found and the influence law of the interactions on different types of topological phases are revealed. The quantum phase diagram of the system under these interactions is finally given.