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

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.

arXiv comment5 pages, 7 figures

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