We study the energy-density dynamics at finite momentum of the two-dimensional Kitaev spin model on the honeycomb lattice. Due to fractionalization of magnetic moments, the energy relaxation occurs through mobile Majorana matter, coupled to a static ${\mathbb{Z}}_2$ gauge field. At finite temperatures, the ${\mathbb{Z}}_2$ flux excitations act as a thermally induced disorder, which strongly affects the energy dynamics. We show that sufficiently far above the flux proliferation temperature, but not yet in the high-temperature classical regime, disordered gauge configurations modify the coherent low-temperature energy-density dynamics into a form which is almost diffusive, with a diffusion kernel that is nearly momentum independent, but which remains retarded, primarily due to the presence of two distinct relaxation channels of particle-hole and particle-particle nature. Relations to the thermal conductivity are clarified. Our analysis is based on complementary calculations in the low-temperature homogeneous gauge configuration and a mean-field treatment of thermal gauge fluctuations, valid above the flux proliferation temperature.

• Received 15 March 2021
• Accepted 30 August 2021

DOI:https://doi.org/10.1103/PhysRevB.104.104424