Kibble-Zurek behavior in one-dimensional disordered topological insulators

Abstract

The discovery of nonlocal order parameters in real space provides a feasible scheme for studying dynamical critical behavior in topological systems. We study the critical phenomena in the one-dimensional Su-Schrieffer-Heeger (SSH) model by investigating the inhomogeneities in the local winding number in real space. By slowly quenching the system across the topological phase transition during a finite time interval, we find that the length scale defined through the local winding number satisfies the Kibble-Zurek mechanism. In contrast to the density of excitation, the scaling of this length scale is in full analog to the behavior of traditional continuous phase transitions with local order parameter and spontaneous symmetry breaking. In addition, the critical behavior and Kibble-Zurek mechanism in the generalized SSH with next-nearest-neighbor hopping are also studied. These results extend our understanding to the Kibble-Zurek mechanism and topological phase transition in nonequilibrium.