Fragile spin liquid in three dimensions

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.

References in corpus (12)

• Local stabilizer codes in three dimensions without string logical operators
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Why spin ice obeys the ice rules
• Three dimensional resonating valence bond liquids and their excitations
• Gapless Bosonic Excitation without symmetry breaking: Novel Algebraic Spin liquid with soft Gravitons
• Fracton topological phases from strongly coupled spin chains
• Fate of partial order on the trillium and distorted windmill lattices
• Topological Route to New and Unusual Coulomb Spin Liquids
• A fractionalised "${\mathbb{Z}}_2$" classical Heisenberg spin liquid
• Irrational moments and signatures of higher-rank gauge theories in diluted classical spin liquids
• Classical spin models of the windmill lattice and their relevance for PbCuTe${}_2$O${}_6$
• Magnetic excitation spectrum and Hamiltonian of the quantum spin chain BaCuTe2O6

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• Chiral order emergence driven by quenched disorder
• Classical fracton spin liquid and Hilbert space fragmentation in a 2D spin-$1/2$ model
• Multistage development of short-range spin correlations and weak magnetic order in the two coupled trillium lattices of K2Fe2(MoO4)(PO4)2
• Unconventional Spin Dynamics and Supersolid Excitations in the Triangular-Lattice XXZ Model