Loschmidt Amplitude Spectrum in Dynamical Quantum Phase Transitions*

The theory of dynamical quantum phase transitions (DQPT) has been a paradigm in the study of many-body quantum dynamics. With the great success of theoretical descriptions supporting the experiments, the reasoning of how DQPT occur is yet to be stated. To that, we propose a scheme called "Loschmidt amplitude spectrum" to study the dynamics. Upon investigating the spectral properties of several quenches, we analytically and numerically reveal the mechanics of DQPT for both integrable and non-integrable models. We demonstrate that the former involves a sudden population migration of momentum quasiparticles, whereas the latter alters the distribution of states having different magnetization. For the integrable model, we also show that the spectral dynamics of Loschmidt quantities behaves more violently than the ground-state quantity, where nonanalyticities can be spotted during quench within the same phase. We expect the proposed scheme is applicable to any model for in-depth analysis and manages to reveal fundamental knowledge about DQPT.