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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.
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We numerically study quenches from a fully ordered state to the ferromagnetic regime of the chiral $mathbb{Z}_3$ clock model, where the physics can be understood in terms of sparse domain walls of six flavors. As in the previously studied models, the spread of entangled domain wall pairs generated by the quench lead to a linear growth of entropy with time, upto a time $ell/2v_g$ in size-$ell$ subsystems in the bulk where $v_g$ is the maximal group velocity of domain walls. In small subsystems located in the bulk, the entropy continues to further grow towards $ln 3$, as domain walls traverse the subsystem and increment the population of the two oppositely ordered states, restoring the $mathbb{Z}_3$ symmetry. The latter growth in entropy is seen also in small subsystems near an open boundary in a non-chiral clock model. In contrast to this, in the case of the chiral model, the entropy of small subsystems near an open boundary saturates. We rationalize the difference in behavior in terms of qualitatively different scattering properties of domain walls at the open boundary in the chiral model. We also present empirical results for entropy growth, correlation spread, and energies of longitudinal-field-induced bound states of domain wall pairs in the chiral model.
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