Detection of long-range entanglement in gapped quantum spin liquids by local measurements

TL;DR

This paper presents a method to detect topological entanglement entropy in gapped quantum spin liquids using only local two-spin correlators, simplifying the identification of topological order.

Contribution

The authors demonstrate that topological entanglement entropy can be extracted from local correlators in a $ ext{Z}_2$ Kitaev spin liquid, providing a practical local measurement approach.

Findings

Accurate extraction of $ ext{log} 2$ topological entropy from local correlators.

Method matches or exceeds the accuracy of the Kitaev-Preskill construction.

Local correlators reflect global topological sectors in the matter Majorana sector.

Abstract

Topological order, reflected in long range patterns of entanglement, is quantified by the topological entanglement entropy (TEE) $\gamma$. We show that for gapped quantum spin liquids (QSL) it is possible to extract $\gamma$ using two-spin local correlators. We demonstrate our method for the gapped $\mathbb{Z}_2$ Kitaev spin liquid on a honeycomb lattice with anisotropic interactions. We show that the $\gamma = \log 2$ for $\mathbb{Z}_2$ topological order can be simply extracted from local two-spin correlators across two different bonds, with an accuracy comparable or higher than the Kitaev-Preskill construction. This implies that the different superselection sectors of $\mathbb{Z}_2$ gauge theory determined by global Wilson loop operators can be fully reflected locally in the matter majorana sector.