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

• Published in: SciPost physics Vol. 10; no. 6; p. 128
• Main Authors: Nathan, Frederik, Abanin, Dmitry, Lindner, Netanel, Berg, Erez, Rudner, Mark Spencer
• Format: Journal Article
• Language: English
• Published: SciPost 01.06.2021
• ISSN: 2542-4653; 2542-4653
• DOI: 10.21468/SciPostPhys.10.6.128

We uncover a new family of few-body topological phases in periodically driven fermionic systems in two dimensions. These phases, which we term correlation-induced anomalous Floquet insulators (CIAFIs), are characterized by quantized contributions to the bulk magnetization from multi-particle correlations, and are classified by a family of integer-valued topological invariants. The CIAFI phases do not require many-body localization, but arise in the generic situation of k-particle localization, where the system is localized (due to disorder) for any finite number of particles up to a maximum number, k. We moreover show that, when fully many-body localized, periodically driven systems of interacting fermions in two dimensions are characterized by a quantized magnetization in the bulk, thus confirming the quantization of magnetization of the anomalous Floquet insulator. We demonstrate our results with numerical simulations.