Dynamical phase transition and scaling in the chiral clock Potts chain

Based on time-dependent variational principle (TDVP) techniques, we investigate the dynamical critical behavior of quantum three-state Potts chains with chiral interactions. Using Loschmidt echo, order parameter, and entanglement entropy as an indicator, we show that as the chiral interaction $\theta$ increases, the first critical time $t_{1}^{*}$ shift towards lower values, indicating a chirality-enhanced dynamical phase transition. Moreover, we perform dynamical scaling for the Loschmidt echo and obtain the critical exponent $\nu$ at the non-conformal critical point. The results show that as the chiral interaction $\theta$ increases, the correlation length exponent $\nu$ decreases, which is similar to the long-range interaction case. Finally, we give a simple physical argument to understand the above numerical results. This work provides a useful reference for further research on many-body physics out of equilibrium with chiral interaction.