Spectroscopic signatures of crystal momentum fractionalization

We consider gapped Z2 spin liquids, where spinon quasiparticles may carry fractional quantum numbers of space group symmetry. In particular, spinons can carry fractional crystal momentum. We show that such quantum number fractionalization has dramatic, spectroscopically accessible consequences, namely enhanced periodicity of the two-spinon density of states in the Brillouin zone, which can be detected via inelastic neutron scattering. This effect is a sharp signature of certain topologically ordered spin liquids and other symmetry enriched topological phases. Considering square lattice space group and time reversal symmetry, we show that exactly four distinct types of spectral periodicity are possible.