Combined approach to analyze and classify families of classical spin liquids

Abstract

Classical spin liquids have been a very active subject of research in the last few years. A very rich variety of cases have been shown to exist, including short-range and algebraic spin liquids displaying dipolar correlations at zero temperature. In this article, we investigate different families of classical spins liquids by combining analytical techniques and Monte Carlo simulations. Our study relies on the Luttinger-Tisza approximation (LTA), which is associated with the constraint vector function in momentum space, whose general properties allow for a classification of different spin liquids. We show that the general properties of the LTA provide a framework for identifying and accurately characterizing the different types of spin liquids in different geometries. We apply our approach to three different families of spin liquids defined on the checkerboard and kagome lattices, which exhibit a remarkable range of situations, including various cases of algebraic and short-range spin liquids. Additionally, we analyze the effective Gauss law emerging from different kinds of spin liquids and identify states that exhibit additional degeneracy lines. The presence of spin-liquid phases and pinch-point singularities are confirmed by Monte Carlo simulations validating our approach. Our study opens up avenues of research in the study of spin liquids, exploring algebraic spin liquids with higher-rank gauge fields and as critical points dividing different types of classical spin liquids.

27 pages, 27 figures

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• Field-induced spin liquid in the decorated square-kagome antiferromagnet nabokoite KCu${}_7$TeO${}_4$(SO${}_4$)${}_5$Cl
• Higher-Rank Spin Liquids and Spin Nematics from Competing Orders in Pyrochlore Magnets
• Classical ${\mathbb{Z}}_2$ spin liquid on the generalized four-color Kitaev model
• Magnetic properties of the spiral spin liquid and surrounding phases in the square lattice XY model
• Quantum effects on pyrochlore higher-rank U(1) spin liquids: Pinch-line singularities, spin nematics, and connections to oxide materials
• Classical spin models of the windmill lattice and their relevance for PbCuTe${}_2$O${}_6$
• Classical and quantum spin liquids
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• Classical fracton spin liquid and Hilbert space fragmentation in a 2D spin-$1/2$ model
• Square ice Coulomb phase as a percolated vertex lattice
• Pinch-line spin liquids as layered Coulomb phases and applications to cubic models
• Entropic selection of magnetization in a frustrated 2D magnetic model
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Decorated cluster lattices: a natural framework for classical spin liquids and flat bands
• Quantum Coulomb Liquids of Different Rank in the Breathing Pyrochlore Antiferromagnet