A fractionalised "$\mathbb{Z}_2$" classical Heisenberg spin liquid

TL;DR

This paper introduces two classical Heisenberg models that exhibit fractionalisation with exponentially decaying correlations, representing a classical analogue of a $ ext{Z}_2$ spin liquid, expanding the understanding of classical spin liquids.

Contribution

The authors present two new classical Heisenberg models showing fractionalisation with exponential decay, akin to a $ ext{Z}_2$ spin liquid, which broadens the classification of classical spin liquids.

Findings

Models exhibit fractionalisation with exponential decay

Classical analogue of $ ext{Z}_2$ spin liquid demonstrated

Suggests systematic search for classical spin liquids

Abstract

Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for \textit{classical} Heisenberg models, only one kind of fractionalised spin liquid phase, the so-called Coulomb or $U(1)$ spin liquid, has until recently been identified: this exhibits algebraic spin correlations and impurity moments, `orphan spins', whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalisation in combination with exponentially decaying correlations. These can be thought of as a classical continuous spin version of a $\mathbb{Z}_2$ spin liquid. Our work suggests a systematic search and classification of classical spin liquids as a worthwhile endeavour.