Topological invariance and global Berry phase in non-Hermitian systems

TL;DR

This paper explores the properties of the complex Berry phase and global Berry phases in non-Hermitian systems, revealing their role in identifying topological invariance and quantum phase transitions, especially at exceptional points.

Contribution

It generalizes the concept of global Berry phases to non-Hermitian systems and demonstrates their effectiveness in detecting topological invariance and phase transitions.

Findings

Global Berry phase Q identifies topological invariance in non-Hermitian models.

Abrupt Berry phase changes indicate quantum phase transitions.

Berry phase behavior relates to exceptional points in parameter space.

Abstract

By studying the topological invariance andBerry phase in non-Hermitian systems, we reveal the basic properties of the complex Berry phase and generalize the global Berry phases Q to identify the topological invariance for non-Hermitian systems.We find thatQcan identify topological invariance in two kinds of non-Hermitian model, the two-level non-Hermitian Hamiltonian and the bipartite dissipative model. For the bipartite dissipative model, an abrupt change of the Berry phase in the parameter space reveals a quantum phase transition and is related to the exceptional points. These results give the basic relationships between the Berry phase and the quantum and topological phase transitions of non-Hermitian systems.