Entanglement spectrum and entropy in Floquet topological matter

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.

arXiv comment18 pages, 13 figures

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• Non-Hermitian Floquet Topological Matter -- A Review
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Floquet topological superconductors with many Majorana edge modes: topological invariants, entanglement spectrum and bulk-edge correspondence
• Topological edge states at Floquet quantum criticality
• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension
• Topological properties of a periodically driven Creutz ladder
• Reentrant topological phases and entanglement scalings in moiré-modulated extended Su-Schrieffer-Heeger Model
• Quantum geometry and geometric entanglement entropy of one-dimensional Floquet topological matter
• Floquet Möbius topological insulators
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems