Multiparty entanglement loops in quantum spin liquids

Quantum spin liquids 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 these phases. Here, we show that the multiparty entanglement of quantum spin liquids can be resolved via entanglement microscopy. We find that in contrast to conventional matter, the genuine multiparty entanglement between spins is absent in the smallest subregions, a phenomenon we call entanglement frustration. Instead, multiparty entanglement 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 quantum spin liquids on the honeycomb and Kagome lattices, as well as with string-net wavefunctions hosting abelian or non-abelian anyons. Our results provide a framework for understanding fractionalization and the means by which gauge bosons encode quantum information, suggesting that entanglement loops are a universal property of quantum gauge theories.