Kibble-Zurek Behavior in the Boundary-obstructed Phase Transitions

TL;DR

This paper investigates the nonadiabatic dynamics of a 2D higher-order topological insulator during boundary-obstructed phase transitions, revealing boundary condition-dependent scaling laws and challenging the traditional Kibble-Zurek mechanism.

Contribution

It demonstrates that boundary conditions significantly alter the Kibble-Zurek scaling exponents in boundary-obstructed topological phase transitions, introducing an effective dimension concept.

Findings

Scaling exponent is 1/2 for hybridized and open boundaries.

Scaling exponent is 2 for periodic boundaries.

Boundary effects modify the applicability of the Kibble-Zurek mechanism.

Abstract

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 $d=2$.