Space group symmetry fractionalization in a chiral kagome Heisenberg antiferromagnet

TL;DR

This paper predicts and verifies the pattern of space group symmetry fractionalization in a chiral kagome spin liquid, providing a practical method for detection in numerical simulations, thus advancing understanding of fractional quantum numbers in spin liquids.

Contribution

It introduces a theoretical prediction for symmetry fractionalization patterns in a kagome chiral spin liquid and demonstrates a simple detection method compatible with DMRG simulations.

Findings

Theoretical prediction matches numerical results.

Detection method is effective in finite-size numerics.

Provides insights into fractional quantum numbers in spin liquids.

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.