Classification of SPT phases of 1+1 non-hermitian system


Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity

Wenjie Xi, Zhi-Hao Zhang, Zheng-Cheng Gu, Wei-Qiang Chen

Abstract: Topological phases in non-Hermitian systems have become a fascinating subject recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian systems. We begin with the non-Hermitian generalization of Su-Schrieffer-Heeger(SSH) model and discuss its many body topological Berry phase, which is well defined for any interacting quasi-Hermitian systems(non-Hermitian systems that have real energy spectrum). We then demonstrate that the classifications of topological phases for quasi-Hermitian systems are exactly the same as their Hermitian counterparts. Moreover, we find that unitarity can even emerge for fixed point partition function describing topological phases in 1D non-Hermitian systems with local interactions. Thus we conjecture that for generic 1D interacting non-Hermitian systems, the classification of topological phases are exactly the same as Hermitian systems.