Kibble-Zurek scaling in the quantum Ising chain with a time-periodic perturbation

TL;DR

This paper investigates the robustness of the quantum Kibble-Zurek mechanism in a periodically perturbed quantum Ising chain, finding that the scaling law remains valid despite oscillatory perturbations.

Contribution

The study analytically demonstrates that the quantum Kibble-Zurek scaling persists in a time-periodic transverse field Ising model, even with non-perturbative effects.

Findings

Scaling remains unchanged despite oscillations.

Non-perturbative contributions do not vanish in the adiabatic limit.

QKZM is robust to periodic perturbations.

Abstract

We consider the time-dependent transverse field Ising chain with time-periodic perturbations. Without perturbations, this model is one of the famous models that obeys the scaling in the adiabatic limit predicted by the quantum Kibble-Zurek mechanism (QKZM). However, it is known that when oscillations are added to the system, the non-perturbative contribution becomes larger and the scaling may break down even if the perturbation is small. Therefore, we analytically analyze the density of defects in the model and discuss how much the oscillations affect the scaling. As a result, although the non-perturbative contribution does not become zero in the adiabatic limit, the scaling does not change from the prediction of the QKZM. This indicates that the QKZM is robust to the perturbations.