Detecting crystal symmetry fractionalization from the ground state: Application to ${\mathbb{Z}}_2$ spin liquids on the kagome lattice

Abstract

In quantum spin liquid states, the fractionalized spinon excitations can carry fractional crystal symmetry quantum numbers, and this symmetry fractionalization distinguishes different topologically ordered spin liquid states. In this work we propose a simple way to detect signatures of such crystal symmetry fractionalizations from the crystal symmetry representations of the ground state wave function. We demonstrate our method on projected ${\mathbb{Z}}_2$ spin liquid wave functions on the kagome lattice, and show that it can be used to classify generic wave functions. Particularly our method can be used to distinguish several proposed candidates of ${\mathbb{Z}}_2$ spin liquid states on the kagome lattice.

main text: 6 pages, 1 figure. supplemental material: 8 pages, 2 figures. Added a few references and the journal reference

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• Symmetry Fractionalization in Two Dimensional Topological Phases
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• Competing Spin Liquid Phases in the S=$\frac{1}{2}$ Heisenberg Model on the Kagome Lattice
• Flux-fusion anomaly test and bosonic topological crystalline insulators
• Diagnosing Fractionalization from the Spin Dynamics of $Z_2$ Spin Liquids on the Kagome Lattice by Quantum Monte Carlo Simulations
• Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors
• Fermionic spinon theory of square lattice spin liquids near the Néel state
• Classification of symmetry fractionalization in gapped ${\mathbb{Z}}_2$ spin liquids
• Space group symmetry fractionalization in a chiral kagome Heisenberg antiferromagnet
• Folding approach to topological orders enriched by mirror symmetry
• Superconductivity from a confinement transition out of a fractionalized Fermi liquid with ${\mathbb{Z}}_2$ topological and Ising-nematic orders
• Spin Liquids and Pseudogap Metals in $SU(4)$ Hubbard Model in Moiré Superlattice
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• Local order parameters for symmetry fractionalization
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• Anomalies in mirror symmetry enriched topological orders
• Detecting symmetry fractionalization in gapped quantum spin liquids by magnetic impurities