Phonon dynamics of Kitaev spin liquid at finite temperatures

When searching for quantum spin liquid physics in Kitaev materials, a general feature to look for is the fractionalization of spins into two types of quasiparticle excitations, which according to the exact solution of the Kitaev model [1] are localized, gapped Z2 fluxes and itinerant Majorana fermions. In pursuit of spin fractionalization, a lot of experimental and theoretical effort has been
devoted to the study of spin dynamics in Kitaev materials through various dynamical probes. Here we propose to study the signatures of the fractionalized excitations in Kitaev materials by exploiting their coupling to lattice vibrations [2]. In particular, we argue that the signatures of fractionalization can be seen in the sound attenuation and the Hall viscosity of acoustic phonons when time-reversal symmetry is broken, e.g., in applied magnetic field. Our analysis based on analytical calculations and Monte Carlo simulations at finite temperature shows that these observables have pronounced temperature dependence reflecting thermal fluctuations of fluxes and their effect on the itinerant Majorana fermions.

[1] A. Kitaev, Annals of Physics 321, 2 (2006).
[2] M.Ye, R. M. Fernandes and N. B. Perkins, Phys. Rev. Research 2, 033180 (2020)