  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.

Statistical Mechanics