Properties of Quantum Spin Liquid in Three-Dimensional Kitaev Model

Here we present a study of the phonon dynamics in the three-dimensional hyperhoneycomb Kitaev spin model. Similar to the famous Kitaev honeycomb model, this model is exactly solvable. For the isotropic coupling parameters, its ground state is quantum spin liquid with a nodal line band structure. In our work, we show that the fractionalized spin excitations of this Kitaev spin liquid have distinct effects on the phonon dynamics, which makes the phonon dynamics a promising tool for exploring the Kitaev spin liquid candidate materials. In particular, we will focus on the signature of the fractionalized excitations in the behavior of the sound attenuation, which describes the phonon decay into the fractionalized excitations. We compute the sound attenuation coefficient by relating it to an imaginary part of the diagonal elements of the phonon self-energy and we find that the angular dependence of the attenuation coefficient.