Space group symmetry fractionalization in a chiral kagome Heisenberg antiferromagnet

Abstract

The anyonic excitations of a spin-liquid can feature fractional quantum numbers under space-group symmetries. Detecting these fractional quantum numbers, which are analogs of the fractional charge of Laughlin quasiparticles, may prove easier than the direct observation of anyonic braiding and statistics. Motivated by the recent numerical discovery of spin-liquid phases in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern of space group symmetry fractionalization in the kagome lattice chiral spin liquid. We provide a method to detect these fractional quantum numbers in finite-size numerics which is simple to implement in DMRG. Applying these developments to the chiral spin liquid phase of a kagome Heisenberg model, we find perfect agreement between our theoretical prediction and numerical observations.

5 pages plus appendix

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Cited by in corpus (13)

• Quantum phases of Rydberg atoms on a kagome lattice
• A Quantum Dipolar Spin Liquid
• Symmetry Fractionalization in Two Dimensional Topological Phases
• Realizing anomalous anyonic symmetries at the surfaces of 3d gauge theories
• Symmetry fractionalization and anomaly detection in three-dimensional topological phases
• Emergent quasi-one-dimensionality in a kagomé magnet: A simple route to complexity
• Gapless chiral spin liquid from coupled chains on the kagome lattice
• Fermionization of Bosons in a Flat Band
• Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator
• Determining non-Abelian topological order from infinite projected entangled pair states
• Determining topological order from infinite projected entangled pair states
• Local order parameters for symmetry fractionalization
• Variational methods for characterizing matrix product operator symmetries