  Dynamical quantum phase transitions (DQPTs), which refer to the criticality
in time of a quantum many-body system, have attracted much theoretical and
experimental research interest recently. Despite DQPTs are defined and
signalled by the non-analyticities in the Loschmidt rate, its interrelation
with various correlation measures such as the equilibrium order parameters of
the system remains unclear. In this work, by considering the quench dynamics in
an interacting topological model, we find that the equilibrium order parameters
of the model in general exhibit signatures around the DQPT, in the short time
regime. The first extrema of the equilibrium order parameters are connected to
the first Loschmidt rate peak. By studying the unequal-time two-point
correlation, we also find that the correlation between the nearest neighbors
decays while that with neighbors further away builds up as time grows in the
non-interacting case, and upon the addition of repulsive intra-cell
interactions. On the other hand, the inter-cell interaction tends to suppress
the two-site correlations. These findings could provide us insights into the
characteristic of the system around DQPTs, and pave the way to a better
understanding of the dynamics in non-equilibrium quantum many-body systems.
