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 \(\alpha=1/2\) for hybridized and fully open boundary conditions, and \(\alpha=2\) for periodic boundary condition. We argue that the exponent \(\alpha=1/2\) cannot be explained by the Kibble-Zurek mechanism unless we adopt an effective dimension \(d^{\rm eff}=1\) 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 \(d=2\).