Entanglement spectrum and entropy in Floquet topological matter

TL;DR

This paper investigates the entanglement spectrum and entropy in Floquet topological insulators, establishing links between entanglement properties and topological phases, and providing a framework for analyzing entanglement in driven quantum systems.

Contribution

It introduces a comprehensive method to analyze entanglement spectra in Floquet topological phases, connecting topological invariants with entanglement features in noninteracting fermionic systems.

Findings

Entanglement spectrum reflects topological invariants like winding and Chern numbers.

Correspondence established between entanglement spectrum and edge states.

Framework applied to various symmetry classes and dimensions.

Abstract

Entanglement is one of the most fundamental features of quantum systems. In this work, we obtain the entanglement spectrum and entropy of Floquet noninteracting fermionic lattice models and build their connections with Floquet topological phases. Topological winding and Chern numbers are introduced to characterize the entanglement spectrum and eigenmodes. Correspondences between the spectrum and topology of entanglement Hamiltonians under periodic boundary conditions and topological edge states under open boundary conditions are further established. The theory is applied to Floquet topological insulators in different symmetry classes and spatial dimensions. Our work thus provides a useful framework for the study of rich entanglement patterns in Floquet topological matter.