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 SO(3)-symmetric chiral spin liquid. We provide a method to detect these fractional quantum numbers in finite-size numerics which is simple to implement in the density matrix renormalization group. 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.

The propagation of spin waves in magnetically ordered systems has emerged as a potential means to shuttle quantum information over large distances. Conventionally, the arrival time of a spin wavepacket at a distance, d, is assumed to be determined by its group velocity, v_g. Here, we report time-resolved optical measurements of wavepacket propagation in the Kagome ferromagnet Fe₃Sn₂ that demonstrate the arrival of spin information at times significantly less than d/v_g. We show that this spin wave "precursor" originates from the interaction of light with the unusual spectrum of magnetostatic modes in Fe₃Sn₂. Related effects may have far-reaching consequences toward realizing long-range, ultrafast spin wave transport in both ferromagnetic and antiferromagnetic systems.