Biorthogonal dynamical quantum phase transitions in non-Hermitian systems

By using biorthogonal bases, we construct a complete framework for biorthogonal dynamical quantum phase transitions in non-Hermitian systems. With the help of associated state which is overlooked previously, we define the automatically normalized biorthogonal Loschmidt echo. This approach is capable of handling arbitrary non-Hermitian systems with complex eigenvalues, which naturally eliminates the negative value of Loschmidt rate obtained without the biorthogonal bases. Taking the non-Hermitian Su-Schrieffer-Heeger model as a concrete example, a peculiar $1/2$ change in biorthogonal dynamical topological order parameter, which is beyond the traditional dynamical quantum phase transitions is observed. We also find the periodicity of biorthogonal dynamical quantum phase transitions depend on whether the two-level subsystem at the critical momentum oscillates or reaches a steady state.Comment: 8 pages, 5 figure