  Much has been learned regarding dynamical quantum phase transition (DQPT) due
to sudden quenches across quantum critical points in traditional quantum
systems. However, not much has been explored when a system undergoes a
localization-delocalization transition. Here, we study one dimensional
fermionic systems in presence of a quasi-periodic potential, which induces
delocalization-localization transition even in 1D. We show signatures of DQPT
in the many-body dynamics, when quenching is performed between phases belonging
to different universality classes. We investigate how the non-analyticity in
the dynamical free energy gets affected with filling fractions in the bare
system and, further, study the fate of DQPT under interaction. Strikingly,
whenever quenching is performed from the low-entangled localized phase to the
high-entangled delocalized phase, our studies suggest an intimate relationship
between DQPT and the rate of the entanglement growth -- Faster growths of
entanglement entropy ensures quicker manifestation of the non-analiticties in
the many-body dynamical free energy.
