  We study the nonequilibrium dynamics of the extended toric code model (both
ordered and disordered) to probe the existence of the dynamical quantum phase
transitions (DQPTs). We show that in the case of the ordered toric code model,
the zeros of Loschmidt overlap (generalized partition function) occur at
critical times when DQPTs occur, which is confirmed by the nonanalyticities in
the dynamical counter-part of the free-energy density. Moreover, we show that
DQPTs occur for any non-zero field strength if the initial state is the excited
state of the toric code model. In the disordered case, we show that it is
imperative to study the behavior of the first time derivative of the dynamical
free-energy density averaged over all the possible configurations, to
characterize the occurrence of a DQPTs in the disordered toric code model since
the disorder parameter itself acts as a new artificial dimension. We also show
that for the case where anyonic excitations are present in the initial state,
the conditions for a DQPTs to occur are the same as what happens in the absence
of any excitation.
