# Nonequilibrium critical dynamics in the quantum chiral clock model

## TL;DR

This study investigates the nonequilibrium critical dynamics of the quantum chiral clock model, verifying finite-time scaling with a non-integer dynamic exponent and determining critical exponents, including effects of thermal fluctuations.

## Contribution

It is the first to numerically determine the critical exponents $eta$ and $ ext{delta}$ for the quantum chiral clock model and to analyze dynamic scaling under thermal effects.

## Key findings

- Finite-time scaling holds for non-integer dynamic exponent $z$.
- Critical exponents $eta$ and $ ext{delta}$ are numerically determined.
- Thermal effects influence the dynamic scaling behavior.

## Abstract

In this paper we study the driven critical dynamics in the three-state quantum chiral clock model. This is motivated by a recent experiment, which verified the Kibble-Zurek mechanism and the finite-time scaling in a reconfigurable one-dimensional array of $^{87}$Rb atoms with programmable interactions. This experimental model shares the same universality class with the quantum chiral clock model and has been shown to possess a nontrivial non-integer dynamic exponent $z$. Besides the case of changing the transverse field as realized in the experiment, we also consider the driven dynamics under changing the longitudinal field. For both cases, we verify the finite-time scaling for a non-integer dynamic exponent $z$. Furthermore, we determine the critical exponents $\beta$ and $\delta$ numerically for the first time. We also investigate the dynamic scaling behavior including the thermal effects, which are inevitably involved in experiments. From a nonequilibrium dynamic point of view, our results strongly support that there is a direct continuous phase transition between the ordered phase and the disordered phase. Also, we show that the method based on the finite-time scaling theory provides a promising approach to determine the critical point and critical properties.