Trace Index and Spectral Flow in the Entanglement Spectrum

TL;DR

This paper explores how spectral flow in the entanglement spectrum of topological insulators reveals topological invariants, linking entanglement properties with edge states and quantum Hall physics.

Contribution

It introduces the concept of trace index as a new topological invariant derived from entanglement spectra and presents methods to identify spectral flow signatures.

Findings

Trace index correlates with spectral flow in topological insulators.

Spectral flow signatures can be extracted from entanglement spectra.

Connection established between entanglement properties and quantum Hall physics.

Abstract

We investigate the entanglement spectra of topological insulators which manifest edge states on a lattice with spatial boundaries. In the physical energy spectrum, a subset of the edge states that intersect the Fermi level translates to discontinuities in the trace of the single-particle entanglement spectrum, which we call a `trace index'. We find that any free-fermion topological insulator that exhibits spectral flow has a non-vanishing trace index, which provides us with a new description of topological invariants. In addition, we identify the signatures of spectral flow in the single-particle and many-body entanglement spectrum; in the process we present new methods to extract topological invariants and establish a connection between entanglement and quantum Hall physics.