Subexponential critical slowing-down at a Floquet time-crystal phase transition
Wenqian Zhang, WU Ya, Xingze Qiu +2 more
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 the 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 temporal coarse-grained correlation function, whose relaxation time diverges at the critical point revealing the CSD. This is demonstrated by investigating the Floquet dynamics of a one-dimensional disordered spin chain. Through finite-size scaling analysis, we show that the relaxation time has a universal subexponential 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.
arXiv:2301.06872•Physical review. B./Physical review. B•Jul 21, 2023•2 citations