Clean two-dimensional Floquet time-crystal

TL;DR

This paper demonstrates the existence of a two-dimensional Floquet time-crystal in the quantum Ising model, showing long-lived stability of discrete time-translation symmetry breaking in a finite-temperature, pre-thermal regime despite energy absorption.

Contribution

It provides the first evidence of a 2D Floquet time-crystal with a pre-thermal phase, using exact diagonalization and tensor-network methods, highlighting stability mechanisms at finite temperature.

Findings

Existence of a 2D Floquet time-crystal phase.

Long-lived stability of magnetic domains at finite temperature.

Non-perturbative change in decay rate with deviations from perfect spin flips.

Abstract

We consider the two-dimensional quantum Ising model, in absence of disorder, subject to periodic imperfect global spin flips. We show by a combination of exact diagonalization and tensor-network methods that the system can sustain a spontaneously broken discrete time-translation symmetry. Employing careful scaling analysis, we show the feasibility of a two-dimensional discrete time-crystal (DTC) pre-thermal phase. Despite an unbounded energy pumped into the system, in the high-frequency limit, a well-defined effective Hamiltonian controls a finite-temperature intermediate regime, wherein local time averages are described by thermal averages. As a consequence, the long-lived stability of the DTC relies on the existence of a long-range ordeblack phase at finite temperature. Interestingly, even for large deviations from the perfect spin flip, we observe a non-perturbative change in the decay rate of the order parameter, which is related to the long-lived stability of the magnetic domains in 2D.