  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.
