Phonon dynamics in the Kitaev spin liquid

The search for fractionalization in quantum spin liquids largely relies on their decoupling with the environment. However, the spin-lattice interaction is inevitable in a real setting. While the Majorana fermion evades a strong decay due to the gradient form of spin-lattice coupling, the study of the phonon dynamics may serve as an indirect probe of fractionalization in a quantum spin liquid. We show that the signatures of fractionalization of the Kitaev spin liquid can be seen in the sound attenuation and the Hall viscosity: the former describes the phonon decay into the fractionalized excitations, and the latter is the leading order time-reversal symmetry breaking effect on the acoustic phonon. This talk is based on two papers: the analytical calculations in the low-temperature zero-flux sector [1], and numerical calculations in the inhomogeneous flux sectors at intermediate and high temperatures [2].