## SciPost Submission Page

# Hierarchy of many-body invariants and quantized magnetization in anomalous Floquet insulators

### by Frederik Nathan, Dmitry A. Abanin, Netanel H. Lindner, Erez Berg, Mark S. Rudner

### Submission summary

As Contributors: | Frederik Nathan |

Arxiv Link: | https://arxiv.org/abs/1907.12228v1 |

Date submitted: | 2019-08-28 |

Submitted by: | Nathan, Frederik |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Quantum Physics |

### Abstract

The anomalous Floquet insulator (AFI) is an intrinsically nonequilibrium topological phase that arises in disordered, periodically driven systems. In the noninteracting case, the nontrivial topology of the AFI gives rise to a quantized current at the edge, and a quantized magnetization in the bulk. Recent work indicates that the AFI is compatible with many-body localization, and is thus stable in the presence of interactions. Here we study the bulk topological properties of the AFI in the interacting case. Compared with the non-interacting case, interactions lead to an enrichment of the topological phase diagram: we find that the AFI is characterized by a family of bulk topological invariants, which are encoded in the time-averaged magnetization density operator of the system. A nontrivial value of the $\ell$-th invariant signifies a quantized contribution to the magnetization density in filled regions arising from correlated $\ell$-particle circulating orbits. The non-interacting ''anomalous Floquet-Anderson insulator'' (AFAI) is characterized by a nonzero value of the first invariant, with all higher invariants equal to zero. We discuss novel strongly correlated anomalous phases, with nonzero values of higher invariants, that are topologically distinct from the AFAI.