Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems

TL;DR

This paper demonstrates that certain Floquet phases of matter exhibit absolute stability and spatiotemporal long-range order, maintaining their properties under weak local perturbations and revealing novel oscillatory behaviors in quantum systems.

Contribution

It introduces the concept of absolutely stable Floquet phases that are robust to all weak local deformations, including symmetry-breaking ones, and exhibit spontaneous symmetry breaking of emergent Hamiltonian-dependent symmetries.

Findings

Absolutely stable Floquet phases exist beyond symmetry constraints.

These phases show long-range order in space and time.

Characteristic oscillations of order parameters are observable.

Abstract

Recent work has shown that a variety of novel phases of matter arise in periodically driven Floquet systems. Among these are many-body localized phases which spontaneously break global symmetries and exhibit novel multiplets of Floquet eigenstates separated by quantized quasienergies. Here we show that these properties are stable to all weak local deformations of the underlying Floquet drives -- including those that explicitly break the defining symmetries -- and that the models considered until now occupy sub-manifolds within these larger "absolutely stable" phases. While these absolutely stable phases have no explicit global symmetries, they spontaneously break Hamiltonian dependent emergent symmetries, and thus continue to exhibit the novel multiplet structure. The multiplet structure in turn encodes characteristic oscillations of the emergent order parameter at multiples of the fundamental period. Altogether these phases exhibit a form of simultaneous long-range order in space and time which is new to quantum systems. We describe how this spatiotemporal order can be detected in experiments involving quenches from a broad class of initial states.