Entanglement spectroscopy of anomalous surface states

TL;DR

This paper investigates the entanglement spectra of surface states in topological phases, revealing how anomalies influence their spectral features and proposing a modified spectrum that captures physical edge states.

Contribution

It introduces a new type of entanglement spectrum that accounts for anomalies in surface states of topological insulators, supported by analytical and numerical evidence.

Findings

Modified entanglement spectra reflect physical edge states.

Anomalies dominate the entanglement spectra of surface states.

Analytical and numerical results confirm the proposed spectra's relevance.

Abstract

We study entanglement spectra of gapped states on the surfaces of symmetry-protected topological phases. These surface states carry anomalies that do not allow them to be terminated by a trivial state. Their entanglement spectra are dominated by non-universal features, which reflect the underlying bulk. We introduce a modified type of entanglement spectra that incorporate the anomaly and argue that they correspond to physical edge states between different surface states. We support these arguments by explicit analytical and numerical calculations for free and interacting surfaces of three-dimensional topological insulators of electrons.