Raman spectroscopy of anyons in generic Kitaev spin liquids

Optical probes have emerged as versatile tools for detecting exotic fractionalized phases in quantum materials. We calculate the low-energy Raman response arising from mobile, interacting Ising anyons in the chiral Kitaev spin liquid perturbed by symmetry allowed interactions---a phase relevant to $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ under a magnetic field. At zero temperature, the two-anyon continuum response shows a leading power-law scaling of the intensity near the onset of the signal: $I(\ensuremath{\omega})\ensuremath{\sim}{(\ensuremath{\omega}\ensuremath{-}{E}_{2\ensuremath{\sigma}}^{0})}^{\frac{1}{8}}$ for linear and parallel-circular polarization channels, where ${E}_{2\ensuremath{\sigma}}^{0}$ is the two-particle gap. Strong corrections due to short-range interactions arise at order $1/4$. For cross-circularly polarized channels, the scaling is given by $I(\ensuremath{\omega})\ensuremath{\sim}{(\ensuremath{\omega}\ensuremath{-}{E}_{2\ensuremath{\sigma}}^{0})}^{|l\ifmmode\pm\else\textpm\fi{}1/8|}$, where the value of $l=0,1,2$ is determined by the number of minima in the single anyon dispersion. The exponents are directly related to the topological spin of Ising anyons ${\ensuremath{\theta}}_{\ensuremath{\sigma}}=\ensuremath{\pi}/8$, describing their exchange statistics. Our theory generalizes to spectral probes of anyonic quasiparticles with multiple band minima in other quantum liquids. Interaction between anyons may also induce bound states, resulting in sharp peaks that show strong polarization dependence.