Finite-momentum energy dynamics in a Kitaev magnet

TL;DR

This paper investigates the finite-momentum energy dynamics in a two-dimensional Kitaev spin model, revealing how fractionalization and gauge disorder influence energy relaxation and diffusion processes.

Contribution

It introduces a detailed analysis of energy-density dynamics at finite momentum in the Kitaev model, accounting for gauge disorder effects and fractionalization.

Findings

Energy relaxation occurs via mobile Majorana fermions coupled to a static gauge field.

Gauge disorder at finite temperatures induces a transition to nearly diffusive energy dynamics.

The study clarifies the relationship between energy dynamics and thermal conductivity in the model.

Abstract

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 an emergent disorder, which strongly affects the energy dynamics. We show that sufficiently far above the flux proliferation temperature, but not yet in the classical regime, gauge disorder modifies the coherent low-temperature energy-density dynamics into a form which is almost diffusive, with hydrodynamic momentum scaling of a diffusion-kernel, which however remains retarded, primarily due to the presence of two distinct relaxation channels of particle-hole and particle-particle nature. Relations to thermal conductivity are clarified. Our analysis is based on complementary calculations in the low-temperature homogeneous gauge and a mean-field treatment of thermal gauge fluctuations, valid at intermediate and high temperatures.