Multiparty entanglement loops in quantum spin liquids

TL;DR

This paper investigates the complex multiparty entanglement structures in quantum spin liquids, revealing that genuine multiparty entanglement is absent in small regions and instead forms collective loops, providing new insights into quantum gauge theories.

Contribution

It uncovers the role of entanglement loops in quantum spin liquids and demonstrates their universality in quantum gauge theories, advancing understanding of fractionalization and quantum information encoding.

Findings

Genuine multiparty entanglement is absent in small subregions of QSLs.

Entanglement arises solely in loop structures within QSLs.

Entanglement loops are a universal feature of quantum gauge theories.

Abstract

Quantum spin liquids (QSLs) give rise to exotic emergent particles by weaving intricate entanglement patterns in the underlying electrons. Bipartite measures between subregions can detect the presence of anyons, but little is known about the full entanglement structure of QSLs. Here, we study the multiparty entanglement of QSLs via entanglement microscopy. We find that in contrast to conventional matter, the genuine multiparty entanglement (GME) between spins is absent in the smallest subregions, a phenomenon we call "entanglement frustration". Instead, GME is more collective, and arises solely in loops. By exploiting exact results and large-scale numerics, we confirm these properties in various gapped and gapless QSLs realised in physically motivated Hamiltonians, as well as with string-net wavefunctions hosting abelian or non-abelian anyons. Our results shed new light on the phase diagram of Kitaev's honeycomb model in a Zeeman field, and the Kagome Heisenberg model under various perturbations. Going beyond QSLs, we provide evidence that entanglement loops are a universal property of quantum gauge theories. This leads to a new understanding of fractionalization, and the means by which gauge bosons encode quantum information.