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

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.

19 pages, 10 figures

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Cited by in corpus (10)

• Thermal Hall effect incorporating magnon damping in localized spin systems
• Thermal Hall Effect of Magnons from Many-Body Skew Scattering
• Topological phase transitions and thermal Hall effect in a noncollinear spin texture
• Interaction-induced nonlinear magnon transport in noncentrosymmetric magnets
• Long-lived Zone-boundary Magnons in an Antiferromagnet
• Formulation of spin Nernst effect for spin-nonconserving insulating magnets
• Spin Nernst and thermal Hall effects of topological triplons in quantum dimer magnets on the maple-leaf and star lattices
• Quantum selection of order and dynamic properties of Kitaev-Heisenberg ferromagnet on a triangular lattice
• Scattering Theory of Chiral Edge Modes in Topological Magnon Insulators
• Topological magnons in a non-coplanar magnetic order on the triangular lattice