Kibble-Zurek mechanism for dissipative discrete time crystals

TL;DR

This paper demonstrates that the Kibble-Zurek mechanism applies to open systems transitioning into discrete time crystals, showing universal scaling laws and verifying predictions in classical and quantum models.

Contribution

It extends the Kibble-Zurek mechanism to dissipative open systems and provides analytical and numerical validation in classical and quantum models.

Findings

KZM signatures observed in DTC transitions include power-law defect scaling.

Universal behavior linked to dissipative linear parametric oscillator models.

Validation of KZM in both classical Sine-Gordon and quantum Dicke lattice models.

Abstract

We demonstrate that the Kibble-Zurek mechanism (KZM) holds for open systems transitioning from a disordered phase to a discrete time crystal (DTC). Specifically, we observe the main signatures of the KZM when the system is quenched into a DTC, which are the characteristic power-law scaling with quench time of the number of spatial defects and the transition delay measured from the time at which the system crosses the critical point. We show analytically that this universal behavior can be traced back to how systems that can be mapped onto a dissipative linear parametric oscillator (DLPO) satisfy the adiabatic-impulse (AI) approximation, evinced by the divergence of the relaxation time of the DLPO near a critical point. We verify our predictions in both the classical and quantum regimes by considering two systems: the Sine-Gordon model, which is a paradigmatic system for emulating classical DTCs; and the open Dicke lattice model, an array of spin-boson systems subjected to quantum fluctuations. For both systems, the DTCs can be tuned from a ferromagnetic to an antiferromagnetic order by varying the driving frequency, thus allowing us to test the validity of KZM for arbitrary spatiotemporal ordering.