Toy model of boundary states with spurious topological entanglement entropy

TL;DR

This paper investigates conditions under which boundary states in topologically trivial systems produce false signals in topological entanglement entropy, revealing a link to symmetry-protected topological phases and presenting a boundary state that defies this pattern.

Contribution

It identifies the specific boundary conditions that lead to spurious topological entanglement entropy and introduces a boundary state that challenges existing understanding of these contributions.

Findings

Spurious contributions occur when boundary states are in non-trivial SPT phases.

A stabilizer boundary state with non-zero spurious entropy can exist outside SPT phases.

The study clarifies the relationship between boundary states and topological entanglement entropy.

Abstract

Topological entanglement entropy has been extensively used as an indicator of topologically ordered phases. We study the conditions needed for two-dimensional topologically trivial states to exhibit spurious contributions that contaminates topological entanglement entropy. We show that if the state at the boundary of a subregion is a stabilizer state, then it has a non-zero spurious contribution to the region if and only if, the state is in a non-trivial one-dimensional $G_1\times G_2$ symmetry-protected-topological (SPT) phase. However, we provide a candidate of a boundary state that has a non-zero spurious contribution but does not belong to any such SPT phase.