1D Many-body localized Floquet systems II: Symmetry-Broken phases

TL;DR

This paper classifies symmetry-broken phases in one-dimensional many-body localized Floquet systems, revealing they correspond to elements of the symmetry group's center, extending understanding of Floquet phases beyond unbroken symmetry cases.

Contribution

It introduces a classification scheme for symmetry-broken Floquet phases in 1D many-body localized systems based on the center of the symmetry group.

Findings

Floquet phases correspond to elements of the center of the symmetry group

Classification extends to higher dimensions

Builds on previous work on unbroken symmetry phases

Abstract

Recent work suggests that a sharp definition of `phase of matter' can be given for periodically driven `Floquet' quantum systems exhibiting many-body localization. In this work we propose a classification of the phases of interacting Floquet localized systems with (completely) spontaneously broken symmetries -- we focus on the one dimensional case, but our results appear to generalize to higher dimensions. We find that the different Floquet phases correspond to elements of $Z(G)$, the centre of the symmetry group in question. In a previous paper we offered a companion classification of unbroken, i.e., paramagnetic phases.