Entanglement Entropy as a Portal to the Physics of Quantum Spin Liquids

TL;DR

This paper reviews how quantum entanglement, especially topological entanglement entropy, provides insights into the non-local order, anyonic quasiparticles, and emergent excitations in quantum spin liquids, which lack conventional order parameters.

Contribution

It highlights the role of entanglement measures in diagnosing and characterizing various exotic properties of quantum spin liquids, including topological order and fractionalized excitations.

Findings

Topological entanglement entropy diagnoses non-local order in QSLs.

Entanglement detects anyonic quasiparticles and braiding statistics.

Size dependence of entanglement reveals emergent fermionic spinons in gapless QSLs.

Abstract

Quantum Spin Liquids (QSLs) are phases of interacting spins that do not order even at the absolute zero temperature, making it impossible to characterize them by a local order parameter. In this article, we review the unique view provided by the quantum entanglement on QSLs. We illustrate the crucial role of Topological Entanglement Entropy in diagnosing the non-local order in QSLs, using specific examples such as the Chiral Spin Liquid. We also demonstrate the detection of anyonic quasiparticles and their braiding statistics using quantum entanglement. In the context of gapless QSLs, we discuss the detection of emergent fermionic spinons in a bosonic wavefunction, by studying the size dependence of entanglement entropy.