Identifying Higher Order Topology and Fractional Corner Charge Using Entanglement Spectra

TL;DR

This paper demonstrates how entanglement spectra can be used to identify higher order topological phases and fractional corner charges in two-dimensional $C_{n}$-symmetric insulators, providing a robust and interaction-preserving method.

Contribution

It introduces a new approach to detect higher order topology and fractional corner charges directly from entanglement spectra without nested Wilson loops.

Findings

Entanglement spectra reveal higher order topological features.

The fractional corner charge can be expressed via protected in-gap states.

Method remains robust under electron-electron interactions that preserve symmetries.

Abstract

We study the entanglement spectrum (ES) of two-dimensional $C_{n}$-symmetric second-order topological insulators (TIs). We show that some characteristic higher order topological observables, e.g., the filling anomaly and its associated fractional corner charge, can be determined from the ES of atomic and fragile TIs. By constructing the relationship between the configuration of Wannier orbitals and the number of protected in-gap states in the ES for different symmetric cuts in real space, we express the fractional corner charge in terms of the number of protected in-gap states of the ES. We show that our formula is robust in the presence of electron-electron interactions as long as the interactions preserve $C_{n}$ rotation symmetry and charge-conservation symmetry. Moreover, we discuss the possible signatures higher order topology in the many-body ES. Our methods allow the identification of some classes of higher order topology without requiring the usage of nested Wilson loops or nested entanglement spectra.