Finite-rate quench in disordered Chern and $Z_2$ topological insulators

TL;DR

This paper investigates how disorder affects the dynamics of topological insulators during finite-rate quantum quenches, revealing conditions for Kibble-Zurek scaling and novel anti-Kibble-Zurek behavior.

Contribution

It demonstrates the impact of disorder on quench dynamics in Chern and Z2 topological insulators, highlighting the breakdown of Kibble-Zurek scaling and proposing local measurements for experimental detection.

Findings

Kibble-Zurek scaling holds in the disordered Haldane model without gap closing.

Disorder induces a gapless region in the Kane-Mele model, destroying Kibble-Zurek scaling.

Anti-Kibble-Zurek behavior observed, with larger excitations at slower quenches.

Abstract

We study the quantum quench of a finite rate across topological quantum transitions in two-dimensional Chern and $Z_2$ topological insulators. We choose the representative Haldane model and the Kane-Mele model to investigate the behavior of excitation density generated by the quench and the impact of disorder on it. For the Haldane model, as long as the spectral gap is not closed by disorder, we find the excitation density at the end of the quench obeys the power-law decay with decreasing quench rate, and the power is consistent with the prediction of the Kibble-Zurek mechanism. By contrast, the Kibble-Zurek scaling of excitation density is absent in the Kane-Mele model once disorder is switched on, which we attribute to the emergence of a disorder-induced gapless region. In particular, the anti-Kibble-Zurek behavior of excitation density, namely, larger excitation density at slower quench, is observed at suitable model parameters. Moreover, we demonstrate that particle's onsite occupation can be used as a local measurable quantity to probe the breakdown of adiabatic evolution. The difference of onsite occupation between the time-evolved state and instantaneous ground state at the end of the quench can successfully capture the key features of excitation density for both the Haldane and Kane-Mele models under periodic and more realistic open boundary conditions, thus facilitating the experimental characterization of the quench dynamics in these models.