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

TL;DR

This paper classifies topological phases in one-dimensional interacting non-Hermitian systems, demonstrating that their classification matches that of Hermitian systems through analysis of the non-Hermitian SSH model and fixed point partition functions.

Contribution

It shows that the topological phase classification for 1D interacting non-Hermitian systems is identical to that of Hermitian systems, extending known classifications.

Findings

Topological phases in quasi-Hermitian systems are classified the same as Hermitian systems.

The many-body topological Berry phase is well-defined for all interacting quasi-Hermitian systems.

Fixed point partition functions in non-Hermitian systems correspond one-to-one with Hermitian counterparts.

Abstract

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 non-Hermitian systems is still exactly the same as Hermitian systems.