Symmetry, Superposition and Fragmentation in Classical Spin Liquids: A General Framework and Applications to Square Kagome Magnets

Abstract

Classical magnets exhibit exotic ground state properties such as spin liquids and fractionalization, promising a manifestation of superposition and projective symmetry construction in classical theory. While system-specific spin-ice or soft-spin models exist, a formal theory for general classical magnets remains elusive. Here, we introduce a generic symmetry group construction built from a vector field in a plaquette of classical spins, demonstrating how classical spins superpose in irreducible representations (irreps) of the symmetry group. The corresponding probability amplitudes serve as order parameters and local spins as fragmented excitations. The formalism offers a many-body vector field representation of diverse ground states, including spin liquids and fragmented phases described as degenerate ensembles of irreps. We apply the theory to a frustrated square Kagome lattice, where spin-ice or soft spin rules are inapt, to describe spin liquids and fragmented phases, all validated through irreps ensembles and unbiased Monte Carlo simulation. Our generic theory sheds light on previously unknown aspects of spin-liquid phases and fragmentation and broadens their applications to other branches of field theory.

Accepted version; 17 pages including references and supplementary material

References in corpus (16)

• "Deconfined" quantum critical points
• Absent pinch points and emergent clusters: further neighbour interactions in the pyrochlore Heisenberg antiferromagnet
• Spin Dynamics in Pyrochlore Heisenberg Antiferromagnets
• Pinwheel valence-bond-crystal ground state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ lattice
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• A fractionalised "${\mathbb{Z}}_2$" classical Heisenberg spin liquid
• Thermodynamics of the spin-half square-kagome lattice antiferromagnet
• Combined approach to analyze and classify families of classical spin liquids
• Order by disorder, without order, in a two-dimensional spin system with O(2) symmetry
• Non-Coplanar Magnetic Orders in Classical Square-Kagome Antiferromagnets
• Magnetism of the $s=1/2$ $J_1$-$J_2$ square-kagome lattice antiferromagnet
• Ferromagnetic Coulomb phase in classical spin ice
• $\require{mhchem}$Quantum paramagnetism in the decorated square-kagome antiferromagnet $\ce{Na6Cu7BiO4(PO4)4Cl3}$
• Classical spin liquids in stacked triangular lattice Ising antiferromagnets
• Static and resonant properties of decorated square kagome lattice compound KCu${}_7$(TeO${}_4$)(SO${}_4$)${}_5$Cl
• The Classical Heisenberg Model on the Centred Pyrochlore Lattice

Cited by in corpus (1)

• Quantum phase diagram of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the square-kagome lattice: a tensor network study