  Recently, dynamical characterization of bulk topology has been experimentally
realized under nonadiabatic sudden quench dynamics. However, it has been shown
that only the topology of final phase can be characterized when the system is
quenched from initial topologically trivial phase. In this paper, taking the
two-dimensional Chern insulator as an example, we make a thorough investigation
of different types of quenching processes under nonadiabatic slow quench
dynamics, and study not only the processes between nontrivial phase and trivial
phase, but also between the phases with different topological invariants. We
find that, under slow quench dynamics, both the initial and final topological
phase can be characterized and the topological invariant can be captured by
time-averaged spin polarization. Moreover, different types of processes can be
distinguished from the special regions where the time-averaged spin
polarization vanishes. All the dynamical characterization schemes are entirely
based on the experimentally measurable quantity time-averaged spin
polarization, and thus one can expect our findings may provide reference for
future experiments.

Quantum Physics