Affine lattice construction of spiral surfaces in classical Heisenberg models

Abstract

Frustration in classical spin models can lead to degenerate ground states without long range order. In reciprocal space, these degeneracies appear as manifolds of wave vectors, their dimensionality increasing with the degree of frustration and the robustness of the disordered spin-liquid state. Here, we present a recipe to explicitly construct Heisenberg models on Bravais lattices with codimension-one manifolds, i.e., lines in two-dimensions and surfaces with different Euler characteristics in three-dimensions. Furthermore, we discuss the role of thermal and quantum fluctuations in stabilizing ordered states.

arXiv comment5 pages, 3 figures, minimal changes in text (including title)

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Cited by in corpus (13)

• Fractional antiferromagnetic skyrmion lattice induced by anisotropic couplings
• Multiloop functional renormalization group approach to quantum spin systems
• Spiral spin-liquid on a honeycomb lattice
• Generic Spiral Spin Liquids
• Degenerate manifolds, helimagnets, and multi-$\mathbf{Q}$ chiral phases in the classical Heisenberg antiferromagnet on the face-centered-cubic lattice
• Low energy structure of spiral spin liquids
• Projective symmetry group classifications of quantum spin liquids on the simple cubic, body centered cubic, and face centered cubic lattices
• Line-Graph Approach to Spiral Spin Liquids
• Helical superfluid in a frustrated honeycomb Bose-Hubbard model
• Competing orders in a frustrated Heisenberg model on the Fisher lattice
• Frustrated magnets in the limit of infinite dimensions: dynamics and disorder-free glass transition
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• Codimension-Two Spiral Spin-Liquid in the Effective Honeycomb-Lattice Compound Cs${}_3$Fe${}_2$Cl${}_9$