Classification of symmetry fractionalization in gapped ${\mathbb{Z}}_2$ spin liquids

Abstract

In quantum spin liquids, fractional spinon excitations carry half-integer spins and other fractional quantum numbers of lattice and time-reversal symmetries. Different patterns of symmetry fractionalization distinguish different spin liquid phases. In this work, we derive a general constraint on the symmetry fractionalization of spinons in a gapped spin liquid, realized in a system with an odd number of spin-$1/2$ per unit cell. In particular, when applied to kagome/triangular lattices, we obtain a complete classification of symmetric gapped ${\mathbb{Z}}_2$ spin liquids.

11 pages, 4 figures. v2 published version: minor revisions, and journal reference added

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• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Triangular lattice quantum dimer model with variable dimer density
• Fermionic symmetry fractionalization in (2+1)D
• Competing Spin Liquid Phases in the S=$\frac{1}{2}$ Heisenberg Model on the Kagome Lattice
• Diagnosing Fractionalization from the Spin Dynamics of $Z_2$ Spin Liquids on the Kagome Lattice by Quantum Monte Carlo Simulations
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• Variational Monte Carlo Study of the 1/9 Magnetization Plateau in Kagome Antiferromagnets
• Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis
• Filling constraints on fermionic topological order in zero magnetic field
• Symmetry protected gapless $Z_2$ spin liquids
• Classification of symmetry-enriched topological quantum spin liquids
• Interplay between multi-spin and chiral spin interactions on triangular lattice
• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
• Detecting symmetry fractionalization in gapped quantum spin liquids by magnetic impurities
• Bosonic SET to SPT Transition under Dyonic LSM Theorem