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

TL;DR

This paper identifies a new intermediate regime called the delayed Kibble-Zurek mechanism in open systems, where dissipation causes a delay in the apparent phase transition time during quenches.

Contribution

It introduces the concept of delayed KZM in open systems, demonstrating its universality and proposing an improved method for transition time identification using spatio-temporal data.

Findings

Delayed KZM manifests as a power-law scaling of transition time with quench time.

The phenomenon is demonstrated in the open Dicke model and lattice systems.

The effect is more prominent near criticality and with larger threshold values.

Abstract

We report a new 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 as 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 spatio-temporal information, such as the system's defect number, for identifying the transition time.