Scaling and universality at ramped quench dynamical quantum phase transitions

Abstract

The nonequilibrium dynamics of a periodically driven extended XY model, in the presence of
linear time dependent magnetic filed, is investigated using the notion of dynamical quantum phase
transitions (DQPTs). Along the similar lines to the equilibrium phase transition, the main purpose
of this work is to search the fundamental concepts such as scaling and universality at the ramped
quench DQPTs. We have shown that the critical points of the model, where the gap closing occurs,
can be moved by tuning the driven frequency and consequently the presence/absence of DQPTs
can be flexibly controlled by adjusting the driven frequency. We have uncovered that, for a ramp
across the single quantum critical point, the critical mode at which DQPTs occur is classified into
three regions: the Kibble-Zurek (KZ) region, where the critical mode scales linearly with the square
root of the sweep velocity, pre-saturated (PS) region, and the saturated (S) region where the critical
mode makes a plateau versus the sweep velocity. While for a ramp that crosses two critical points,
the critical modes disclose just KZ and PS regions. On the basis of numerical simulations, we find
that the dynamical free energy scales linerly with time, as approaches to DQPT time, with the
exponent ν = 1 ± 0.01 for all sweep velocities and driven frequencies.