  We study the dynamics of systems quenched through topological quantum phase
transitions and investigate the behavior of the bulk and edge excitations with
various quench rates. Specifically, we consider the Haldane model and
checkerboard model in slow quench processes with distinct band-touching
structures leading to topology changes. The generation of bulk excitations is
found to obey the power-law relation Kibble-Zurek and Landau-Zener theories
predict. However, an anti-Kibble-Zurek behavior is observed in the edge
excitations. The mechanism of excitation generation on edge states is revealed,
which explains the anti-Kibble-Zurek behavior.
