Fragile spin liquid in three dimensions

TL;DR

This paper investigates a three-dimensional classical Heisenberg model on the trillium lattice, revealing a fragile spin liquid with short-range correlations and potential quantum analogs, marking a novel discovery in spin liquid research.

Contribution

It introduces the first example of a purely short-range correlated classical Heisenberg spin liquid in three dimensions on the trillium lattice.

Findings

Realizes a fragile spin liquid in 3D on the trillium lattice

Shows exponential decay of correlations and fractionalization

Suggests a possible $ ext{Z}_2$ quantum spin liquid phase

Abstract

Motivated by the recent appearance of the trillium lattice in the search for materials hosting spin liquids, we study the ground state of the classical Heisenberg model on its linegraph, the trilline lattice. We find that this network realises the recently proposed notion of a fragile spin liquid in three dimensions. Additionally, we analyze the Ising case and argue for a possible $\mathbb{Z}_2$ quantum spin liquid phase in the corresponding quantum dimer model. Like the well-known $U(1)$ spin liquids, the classical phase hosts moment fractionalisation evidenced in the diluted lattice, but unlike these, it exhibits exponential decay both in spin correlations and interactions between fractionalised moments. This provides the first instance of a purely short-range correlated classical Heisenberg spin liquid in three dimensions.