Schwinger boson theory for $S=1$ Kitaev quantum spin liquids

Abstract

The Kitaev model is an exactly solvable model with a quantum spin liquid ground state. While this model was originally proposed as an $S=1/2$ spin model on a honeycomb lattice, extensions to higher-spin systems have recently attracted attention. In contrast to the $S=1/2$ case, such higher-$S$ models are not exactly solvable and remain poorly understood, particularly for spin excitations at finite temperatures. Here, we focus on the $S=1$ Kitaev model, which is proposed to host bosonic quasiparticles. We investigate this model using Schwinger boson mean-field theory, introducing bosonic spinons as fractional quasiparticles by extending bond operators to address anisotropic spin interactions. We determine the mean-field parameters that realize a quantum spin liquid in both ferromagnetic and antiferromagnetic Kitaev models. Based on this ansatz, we calculate dynamical and equal-time spin structure factors. We find that the conventional scheme based on Wick decoupling with respect to spinons to calculate spin correlations, the resultant spin structure factors exhibit a momentum dependence that is not consistent with the sign structure expected from the exchange interaction. To resolve this issue, we propose an alternative evaluation based on decoupling with respect to bond operators. We demonstrate that, in our scheme, this discrepancy is removed, and the momentum dependence of the spin structure factors is consistent with the sign of the exchange constant. We also compute the temperature evolution of the dynamical spin structure factor and find that the zero-temperature continuum splits into two distinct structures as temperature increases, which can be understood in terms of the bandwidth narrowing of spinons. Finally, we clarify why the two decoupling schemes result in different momentum dependences and discuss their relationship to previous studies.