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

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.

Automated summary

A new family of few-body topological phases, termed correlation-induced anomalous Floquet insulators (CIAFIs), have been uncovered in periodically driven fermionic systems in two dimensions. These phases are characterized by quantized contributions to bulk magnetization from multi-particle correlations and are classified by integer-valued topological invariants. The study also shows that periodically driven systems of interacting fermions in two dimensions exhibit quantized magnetization in the bulk when fully many-body localized.