Spurious topological entanglement entropy from subsystem symmetries

TL;DR

This paper reveals that common methods for calculating topological entanglement entropy can be misleading due to long-range string order, and proposes an entropic measure to identify such phases.

Contribution

It identifies the source of spurious contributions in topological entropy calculations and introduces a new entropic quantity as an order parameter for certain phases.

Findings

Spurious contributions can arise even in models with zero correlation length.

Long-range string order causes these spurious contributions.

A new entropic measure can detect the presence of such order.

Abstract

We demonstrate that linear combinations of subregion entropies with canceling boundary terms, commonly used to calculate the topological entanglement entropy, may suffer from spurious nontopological contributions even in models with zero correlation length. These spurious contributions are due to a specific kind of long-range string order, and persist throughout certain subsystem symmetry-protected phases. We introduce an entropic quantity that measures the presence of such order, and hence should serve as an order parameter for the aforementioned phases.