Phonon renormalization in the Kitaev quantum spin liquid

TL;DR

This paper investigates how phonons interact with the fractionalized excitations in the Kitaev quantum spin liquid, revealing temperature-dependent renormalization effects influenced by emergent gauge fields and flux excitations.

Contribution

It provides a detailed analysis of phonon self-energy in the Kitaev model, incorporating thermal flux effects and gauge fluctuations, which was not previously explored.

Findings

Flux excitations significantly modify phonon spectra.

High-temperature flux proliferation broadens phonon features.

Phonon behavior varies with temperature due to gauge fluctuations.

Abstract

We study the self-energy of phonons, magnetoelastically coupled to the two-dimensional Kitaev spin-model on the honeycomb lattice. Fractionalization of magnetic moments into mobile Majorana matter and a static $\mathbb{Z}_{2}$ gauge field lead to a continuum of relaxation processes comprising two channels. Thermal flux excitations, which act as an emergent disorder, strongly affect the phonon renormalization. Above the flux proliferation temperature, the dispersion of a narrow quasiparticle-hole channel is suppressed in favor of broad and only weakly momentum dependent features, covering large spectral ranges. 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.