Abelian Floquet symmetry-protected topological phases in one dimension

TL;DR

This paper classifies and characterizes one-dimensional Floquet topological phases protected by Abelian symmetries, revealing new dynamical phases with edge modes linked to bulk invariants in time-dependent quantum systems.

Contribution

It provides a classification of Floquet symmetry-protected topological phases in 1D interacting systems and introduces models and a loop construction for realizing these phases.

Findings

Topological phases characterized by a bulk invariant related to unitary evolution.

Edge modes in quasienergy spectrum indicate nontrivial phases.

Bulk-edge correspondence established for dynamical phases.

Abstract

Time-dependent systems have recently been shown to support novel types of topological order that cannot be realised in static systems. In this paper, we consider a range of time-dependent, interacting systems in one dimension that are protected by an Abelian symmetry group. We classify the distinct topological phases that can exist in this setting and find that they may be described by a bulk invariant associated with the unitary evolution of the closed system. In the open system, nontrivial phases correspond to the appearance of edge modes in the many-body quasienergy spectrum, which relate to the bulk invariant through a form of bulk-edge correspondence. We introduce simple models which realise nontrivial dynamical phases in a number of cases, and outline a loop construction that can be used to generate such phases more generally.