  Quantum phase transition occurs at a quantum critical value of a control
parameter such as the magnetic field in the Ising model in a transverse
magnetic field (ITF). Recently, it is shown that ramping across the quantum
critical point generates non-analytic behaviors in the time evolution of a
closed quantum system in the thermodynamic limit at zero temperature. The
mentioned phenomenon is called the dynamical quantum phase transition (DQPT).
Here, we consider the one-dimensional (1D) ITF model with added the
Dzyaloshinskii-Moriya interaction (DMI). Using the fermionization technique,
the Hamiltonian is exactly diagonalized. Although the DM interaction induces
chiral phase in the ground state phase diagram of the model, the study of the
rate function of the return probability has proven that the DMI does not affect
in the DQPT. We conclude accordingly that the ramping across the quantum
critical point is not a necessary and sufficient condition for DQPT.
