The Sub-Exponential Critical Slowing Down at Floquet Time Crystal Phase Transition

TL;DR

This paper investigates the critical slowing down at the phase transition of Floquet time crystals, revealing a universal sub-exponential divergence of relaxation time, contrasting with traditional power-law behavior in equilibrium systems.

Contribution

It introduces a space-time correlation function to describe critical dynamics and demonstrates sub-exponential scaling of relaxation time near the transition in disordered spin chains.

Findings

Relaxation time diverges sub-exponentially at the critical point.

Universal scaling behavior observed in Floquet time crystal transition.

Results are testable in current quantum simulation experiments.

Abstract

Critical slowing down (CSD) has been a trademark of critical dynamics for equilibrium phase transitions of a many-body system, where the relaxation time for the system to reach thermal equilibrium or quantum ground state diverges with system size. The time crystal phase transition has attracted much attention in recent years for it provides a scenario of phase transition of quantum dynamics, unlike conventional equilibrium phase transitions. Here, we study critical dynamics near the Floquet time crystal phase transition. Its critical behavior is described by introducing a space-time coarse grained correlation function, whose relaxation time diverges at the critical point revealing the CSD. This is demonstrated by investigating the Floquet dynamics of one-dimensional disordered spin chain. Through finite-size scaling analysis, we show the relaxation time has a universal sub-exponential scaling near the critical point, in sharp contrast to the standard power-law behavior for CSD in equilibrium phase transitions. This prediction can be readily tested in present quantum simulation experiments.