Kibble-Zurek Behavior in the Boundary-obstructed Phase Transitions

We study the nonadiabatic dynamics of a two-dimensional higher-order topological insulator when the system is slowly quenched across the boundary-obstructed phase transition, which is characterized by edge band gap closing. We find that the number of excitations produced after the quench exhibits power-law scaling behaviors with the quench rate. Boundary conditions can drastically modify the scaling behaviors: The scaling exponent is found to be =1/2 for hybridized and fully open boundary conditions, and =2 for periodic boundary condition. We argue that the exponent =1/2 cannot be explained by the Kibble-Zurek mechanism unless we adopt an effective dimension d^ eff=1 instead of the real dimension d=2. For comparison, we also investigate the slow quench dynamics across the bulk-obstructed phase transitions and a single multicritical point, which obeys the Kibble-Zurek mechanism with dimension d=2.