Flavor-wave theory with quasiparticle damping at finite temperatures: Application to chiral edge modes in the Kitaev model

TL;DR

This paper develops a finite-temperature flavor-wave theory to analyze quasiparticle excitations and damping in quantum spin models, applying it to the Kitaev model to reveal temperature-dependent damping of chiral edge modes.

Contribution

It extends flavor-wave theory to include quasiparticle damping at finite temperatures, enabling analysis of topological edge modes in complex quantum models.

Findings

Chiral edge modes experience increased damping with temperature.

Quasiparticle collisions cause damping of topological excitations.

Method applicable to various localized electron systems.

Abstract

We propose a theoretical framework to investigate elementary excitations at finite temperatures within a localized electron model that describes the interactions between multiple degrees of freedom, such as quantum spin models and Kugel-Khomskii models. Thus far, their excitation structures have been mainly examined using the linear flavor-wave theory, an SU($N$) generalization of the linear spin-wave theory. These techniques introduce noninteracting bosonic quasiparticles as elementary excitations from the ground state, thereby elucidating numerous physical phenomena, including excitation spectra and transport properties characterized by topologically nontrivial band structures. Nevertheless, the interactions between quasiparticles cannot be ignored in systems exemplified by $S=1/2$ quantum spin models, where strong quantum fluctuations are present. Recent studies have investigated the effects of quasiparticle damping at zero temperature in such models. In our study, extending this approach to the flavor-wave theory for general localized electron models, we construct a comprehensive method to calculate excitation spectra with the quasiparticle damping at finite temperatures. We apply our method to the Kitaev model under magnetic fields, a typical example of models with topologically nontrivial magnon bands. Our calculations reveal that chiral edge modes undergo significant damping in weak magnetic fields, amplifying the damping rate by the temperature increase. This effect is caused by collisions with thermally excited quasiparticles. Since our approach starts from a general Hamiltonian, it will be widely applicable to other localized systems, such as spin-orbital coupled systems derived from multi-orbital Hubbard models in the strong correlation limit.