Long-time properties of generic Floquet systems are approximately periodic with the driving period

TL;DR

This paper proves that in generic large Floquet quantum systems with local interactions, long-time properties like observable expectations and entanglement entropy are approximately periodic with the driving period, indicating that true infinite-time time-crystalline behavior is rare.

Contribution

It establishes that for almost all such systems, long-time properties are approximately periodic, showing that persistent discrete time-crystalline order is not typical.

Findings

Long-time properties are approximately periodic in almost all Floquet systems.

Discrete time-crystalline behavior does not persist indefinitely in generic systems.

The set of systems with non-periodic long-time behavior has measure zero.

Abstract

A Floquet quantum system is governed by a Hamiltonian that is periodic in time. Consider the space of piecewise time-independent Floquet systems with (geometrically) local interactions. We prove that for all but a measure zero set of systems in this space, starting from a random product state, many properties (including expectation values of observables and the entanglement entropy of a macroscopically large subsystem) at long times are approximately periodic with the same period as the Hamiltonian. Thus, in almost every Floquet system of arbitrarily large but finite size, discrete time-crystalline behavior does not persist to strictly infinite time.