Topological invariance and global Berry phase in non-Hermitian systems

By studying the topological invariance and Berry 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 that Q can 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.