Dynamical quantum phase transitions in Stark quantum spin chains

We investigate the nonequilibrium dynamics of one-dimension spin models in the presence of a uniform force. The linear potential induces delocalization-localization transition in the free particles model which is known as the Wannier-Stark effect. We study dynamical quantum phase transition (DQPT) due to sudden global quenches across a quantum critical point when the system undergoes a localization-delocalization transition. In this regard, we consider the XX and XXZ spin chains and explore two types of quenches with and without ramping through the delocalization-localization point. The XX model was mapped to the free fermion particles, so both analytical and numerical results were provided. Results unveil that the dynamical signature of localization-delocalization transition can be characterized by the nonanalyticities in dynamical free energy (corresponds to the zero points in the Loschmit echo). We also explore the interaction effects considering XXZ spin chains, using the time-dependent extension of the numerical DMRG technique. Our results show that depending on the anisotropic parameter $\Delta\lessgtr1.0$, if both the initial and post-quench Hamiltonian are in the same phase or not, DQPTs may happen. Moreover, the interrelation between DQPTs with different correlation measures such as the equilibrium order parameters or entanglement entropy production of the system remains unclear. We provide more analyses on the feature of DQPTs, in both types of quenches, by connecting them to the average local magnetization, entanglement entropy production, and the Schmidt gap.