  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.
