Anomalous Structures of Fisher Zero Lines in Biorthogonal Dynamical Quantum Phase Transitions

Abstract

Fisher zero lines of the Loschmidt amplitude in non-Hermitian quenches can exhibit anomalous structures in the complex time plane, such as divergence, separation, and the restriction of all branches or a specific branch to the real or imaginary axis. Here, we use the biorthogonal framework to reveal the origin of these structures and determine the corresponding critical momentum conditions by analyzing the values of $m_k=\hat{\mathbf{h}}_0\cdot\hat{\mathbf{h}}_1$, the dot product between the normalized prequench and postquench complex Bloch vectors. When Fisher zeros continuously cover the real-time axis, the density of Fisher zeros is further introduced to identify the critical times within these critical regions, at which the rate function becomes nonanalytic. We verify our results in a generalized non-Hermitian SSH model by quenching the Peierls phase and the non-Hermitian gain-loss strength, and also use the Jordan form to analyze the dynamics at postquench exceptional points, where the conventional Fisher zero formula is not applicable.