Varying quench dynamics: the Kibble-Zurek, saturated, and pre-saturated regimes

According to the Kibble-Zurek mechanism, there is a universal power-law relationship between the defect density and the quench rate during a slow linear quench through a critical point. It is generally accepted that a fast quench results in a deviation from the Kibble-Zurek scaling law and leads to the formation of a saturated plateau in the defect density. Our focus is on the transitions of quench dynamics as quench rates vary from slow to very fast limits. Through an in-depth analysis of the transverse Ising chain, we have identified a pre-saturated regime that lies between the saturated and Kibble-Zurek regimes. As we approach the transition point from the saturated to pre-saturated regimes, we notice a change in scaling laws and, with an increase in the initial transverse field, a shrinking of the saturated regime until it disappears. During another transition from the Kibble-Zurek to pre-saturated regimes, we observe an attenuation of the dephasing effect and a change in the behavior of the kink-kink correlation function from a Gaussian decay to an exponential decay.