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

Topological phases in non-Hermitian systems have become fascinating subjects recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian systems. We begin with the non-Hermitian generalization of the Su-Schrieffer-Heeger (SSH) model and discuss its many-body topological Berry phase, which is well defined for all interacting quasi-Hermitian systems (non-Hermitian systems that have real energy spectrum). We then demonstrate that the classification of topological phases for quasi-Hermitian systems is exactly the same as their Hermitian counterparts. Finally, we construct the fixed point partition function for generic 1D interacting non-Hermitian local systems and find that the fixed point partition function still has a one-to-one correspondence to their Hermitian counterparts. Thus, we conclude that the classification of topological phases for generic 1D interacting nonHermitian systems is still exactly the same as Hermitian systems. (c) 2021 Science China Press. Published by Elsevier B.V. and Science China Press. All rights reserved.

Automated summary

This paper investigates the classification of topological phases in 1D interacting non-Hermitian systems, showing that it is exactly the same as their Hermitian counterparts. The study demonstrates the equivalence in topological phases between quasi-Hermitian and Hermitian systems in the context of interacting non-Hermitian local systems.