Apparent delay of the Kibble-Zurek mechanism in quenched open systems

We report an intermediate regime in the quench time, tau q, separating the usual validity of the Kibble-Zurek mechanism (KZM) and its breakdown for rapid quenches in open systems under finite quench protocols. It manifests in the power-law scaling of the transition time with tau q as the system appears to enter the adiabatic regime, even though the ramp is already terminated and the final quench value is held constant. This intermediate regime, which we dub the delayed KZM, emerges due to the dissipation, preventing the system from freezing in the impulse regime. This results in a large delay between the actual time the system undergoes a phase transition and the time inferred from a threshold-based criterion for the order parameter, as done in most experiments. We demonstrate using the open Dicke model and its one-dimensional lattice version that this phenomenon is a generic feature of open systems that can be mapped onto an effective coupled oscillator model. We also show that the phenomenon becomes more prominent near criticality, and its effects on the transition time measurement can be further exacerbated by large threshold values for an order parameter. Due to this, we propose an alternative method for threshold-based criterion which uses the spatiotemporal information, such as the system's defect number, for identifying the transition time.