Entanglement spectrum of topological insulators and superconductors

TL;DR

This paper establishes a precise relationship between the entanglement spectrum of topological insulators and superconductors and their physical edge modes, revealing that degeneracies in the entanglement spectrum indicate gapless edge states.

Contribution

It proves an exact relation linking the ground state entanglement spectrum to the spectrum of edge modes in topological phases, clarifying their connection.

Findings

Degeneracies in the entanglement spectrum correspond to gapless edge modes.

The relation holds for spectrally flattened Hamiltonians.

Provides a theoretical foundation for identifying topological edge states via entanglement spectrum.

Abstract

We study two a priori unrelated constructions: the spectrum of edge modes in a band topological insulator or superconductor with a physical edge, and the ground state entanglement spectrum in an extended system where an edge is simulated by an entanglement bipartition. We prove an exact relation between the ground state entanglement spectrum of such a system and the spectrum edge modes of the corresponding spectrally flattened Hamiltonian. In particular, we show that degeneracies of the entanglement spectrum correspond to gapless edge modes.