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

## TL;DR

This paper introduces a new class of topological phases in driven two-dimensional fermionic systems, characterized by quantized bulk magnetization arising from multi-particle correlations, and classifies them using integer-valued invariants.

## Contribution

It uncovers correlation-induced anomalous Floquet insulators (CIAFIs) and their classification, expanding understanding of topological phases in periodically driven systems without requiring full many-body localization.

## Key findings

- CIAFIs are characterized by quantized bulk magnetization from multi-particle correlations.
- Numerical simulations confirm the quantization of magnetization in fully many-body localized systems.
- The phases are classified by a family of integer-valued topological invariants.

## Abstract

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.