Constrained motion of fractionalized quasiparticles in Kitaev spin liquid

In a quantum spin liquid (QSL), a single spin flip creates fractionalized excitations whose spectral function shows broad features in energy and momentum. Therefore a standard inelastic neutron scattering experiment does not reveal distinct features of a QSL. The question we focus on is whether there is way to detect sharp signatures of a QSL. By analyzing the Kitaev honeycomb model of interacting qubits with anisotropic bond-dependent interactions and anisotropic coupling strength in a magnetic field, away from the exactly solvable limit, we show that the two spin-flip spectral function indeed shows sharp peaks at low energies associated with different anyonic quasiparticles. Further, the momentum dispersion of these anyons at the peak energy shows fracton-like constrained mobility in one dimension. These signatures, the peaks in energy, and the one-dimensional motion, provide a definitive signature of fractionalization in the Kitaev QSL. We propose that the two-spin flip spectral functions should be observable by Raman scattering (for only q=0) and more generally by inelastic light scattering.