Anomalous Floquet Insulators

TL;DR

This paper introduces the anomalous Floquet insulator (AFI), a non-equilibrium topological phase with a many-body localized bulk and thermalizing edge states, expanding understanding of driven quantum systems.

Contribution

It demonstrates the existence and stability conditions of the AFI phase, combining analytical and numerical methods to explore its unique topological and localization properties.

Findings

Bulk can be many-body localized with interactions.

Edge states thermalize and propagate despite bulk localization.

Stable non-uniform density profiles observed over long times.

Abstract

We demonstrate the existence of a two-dimensional anomalous Floquet insulator (AFI) phase: an interacting (periodically-driven) non-equilibrium topological phase of matter with no counterpart in equilibrium. The AFI is characterized by a many-body localized bulk, exhibiting nontrivial micromotion within a driving period, and delocalized (thermalizing) chiral states at its boundaries. For a geometry without edges, we argue analytically that the bulk may be many-body localized in the presence of interactions, deriving conditions where stability is expected. We investigate the interplay between the thermalizing edge and the localized bulk via numerical simulations of an AFI in a geometry with edges. We find that non-uniform particle density profiles remain stable in the bulk up to the longest timescales that we can access, while the propagating edge states persist and thermalize, despite being coupled to the bulk. These findings open the possibility of observing quantized edge transport in interacting systems at high temperature. The analytical approach introduced in this paper can be used to study the stability of other anomalous Floquet phases.