  We study quenching dynamics of a one-dimensional transverse Ising chain with
nearest neighbor antiferromagentic interactions in the presence of a
longitudinal field which renders the model non-integrable. The dynamics of the
spin chain is studied following a slow (characterized by a rate) or sudden
quenches of the longitudinal field; the residual energy, as obtained
numerically using a t-DMRG scheme, is found to satisfy analytically predicted
scaling relations in both the cases. However, analyzing the temporal evolution
of the Loschmidt overlap, we find different possibilities of the presence (or
absence) of dynamical phase transitions (DPTs) manifested in the
non-analyticities of the rate function. Even though the model is
non-integrable, there are {periodic} occurrences of DPTs when the system is
slowly ramped across the quantum critical point (QCP) as opposed to the
ferromagnetic (FM) version of the model; this numerical finding is
qualitatively explained by mapping the original model to an effective
integrable spin model which is appropriate for describing such slow quenches.
Furthermore, concerning the sudden quenches, our numerical results show that in
some cases, DPTs can be present even when the spin chain is quenched within the
same phase or even to the QCP while in some other situations they completely
disappear even after quenching across the QCP. These observations lead us to
the conclusion that it is the change in the nature of the ground state that
determines the presence of DPTs following a sudden quench.
