Relating the entanglement spectrum of noninteracting band insulators to their quantum geometry and topology

TL;DR

This paper investigates the entanglement spectrum of noninteracting band insulators, revealing its connection to quantum geometry and topology, and identifying signatures of topological phases through gapless entanglement spectra.

Contribution

It establishes a link between the entanglement spectrum and quantum geometry, providing new insights into topological phases in band insulators.

Findings

Topological phases exhibit gapless entanglement spectra with an 'entanglement Fermi surface'

Derived a relation between entanglement spectrum and Fubini-Study metric of Bloch states

Illustrated results with models of Chern and Z_2 topological insulators

Abstract

We study the entanglement spectrum of noninteracting band insulators, which can be computed from the two-point correlation function, when restricted to one part of the system. In particular, we analyze a type of partitioning of the system that maintains its full translational symmetry, by tracing over a subset of local degrees of freedom, such as sublattice sites or spin orientations. The corresponding single-particle entanglement spectrum is the band structure of an entanglement Hamiltonian in the Brillouin zone. We find that the hallmark of a nontrivial topological phase is a gapless entanglement spectrum with an "entanglement Fermi surface." Furthermore, we derive a relation between the entanglement spectrum and the quantum geometry of Bloch states contained in the Fubini-Study metric. The results are illustrated with lattice models of Chern insulators and Z_2 topological insulators.