Floquet Topological Order in Interacting Systems of Bosons and Fermions

TL;DR

This paper introduces a new form of dynamical topological order in interacting many-body systems driven periodically, revealing robust edge modes and anomalous transport phenomena applicable to bosons, fermions, and spins.

Contribution

It extends Floquet topological concepts to interacting systems, classifies the associated edge operators, and introduces a framework for dynamical topological order in time-dependent phases.

Findings

Robust anomalous edge operators classified by coprime integers.

Existence of dynamical topological order in many-body localized phases.

Application to a broad class of bosonic, fermionic, and spin systems.

Abstract

Periodically driven noninteracting systems may exhibit anomalous chiral edge modes, despite hosting bands with trivial topology. We find that these drives have surprising many-body analogs, corresponding to class A, which exhibit anomalous charge and information transport at the boundary. Drives of this form are applicable to generic systems of bosons, fermions, and spins, and may be characterized by the anomalous unitary operator that acts at the edge of an open system. We find that these operators are robust to all local perturbations and may be classified by a pair of coprime integers. This defines a notion of dynamical topological order that may be applied to general time-dependent systems, including many-body localized phases or time crystals.