# Slow quenches in Chern insulator ribbons

## TL;DR

This paper studies how slow parameter changes in Chern insulator ribbons affect in-gap state excitations and Hall conductance, revealing a Kibble-Zurek scaling and a faster decay of conductance deviation.

## Contribution

It demonstrates the scaling laws for in-gap excitations and Hall conductance deviations during slow quenches in a specific Chern insulator model with inversion symmetry.

## Key findings

- In-gap state excitation density scales as τ^{-1/2}.
- Hall conductance deviation scales as τ^{-1}.
- Kibble-Zurek mechanism applies to the quench dynamics.

## Abstract

We investigate slow quenches in Chern insulators in ribbon geometry. We consider the Qi-Wu-Zhang model and slowly ramp the parameters (large time of the quench $\tau$) from a non-topological (Chern number = 0) to a topological regime (Chern number $\ne$ 0). In contrast to the Haldane model considered in [L. Privitera and G. E. Santoro, Phys. Rev. B 93, 241406(R) (2016)] earlier, the in-gap state degeneracy point is pinned to an inversion symmetric momentum, which changes the behavior drastically. The density of excitations in the in-gap states scales with the quench time as $\tau^{-1/2}$ as the ramp becomes slow, and the Kibble-Zurek mechanism applies. Despite the slower scaling of the density of in-gap excitations with $\tau$, the Hall conductance after the quench deviates from that of the ground state of the final Hamiltonian by an amount that drops as $\tau^{-1}$.