Chiral bosonic mean-field Ansatz and spin dynamics in spin-1 Kitaev magnets

The Kitaev model is a paradigmatic system for realizing quantum spin liquids, but its higher-spin extensions are not exactly solvable, and their spin dynamics is less well understood than in the spin-1/2 case. In this work, we reexamine a previously introduced triplet-pairing $φ_t = π/2$ phase pattern for the antiferromagnetic $S = 1$ Kitaev model and extend the analysis to weak symmetric off-diagonal exchanges $Γ$ and $Γ'$. Using a bond-operator formulation of Schwinger-boson mean-field theory, we calculate the dynamical spin structure factor for the triplet 0-flux and triplet $π/2$-flux Ansätze with a spin-correlation scheme appropriate for Kitaev interactions. In the pure Kitaev limit, the $π/2$-flux Ansatz yields a flatter spectrum than the 0-flux Ansatz. The real-space spin correlations show that the $π/2$-flux Ansatz suppresses longer-distance correlations more strongly than the 0-flux Ansatz, yielding a correlation pattern closer to the short-ranged form expected in the Kitaev limit. This comparison shows that the flatness of $S(\boldsymbol{q}, ω)$ is tied to short-ranged spin correlations and is therefore an important consistency check, although it is not, by itself, a diagnostic of time-reversal-symmetry breaking. We then study weak off-diagonal exchanges along $Γ' = Γ$ near the pure Kitaev limit, taking the same-sign relation from analyses of candidate spin-1 Kitaev materials. Gapped solutions are obtained within the constrained $π/2$-flux manifold, and the spectra share the qualitative energy- and momentum-space features found by finite-size exact diagonalization. Taken together, these results support the triplet $π/2$-flux chiral bosonic Ansatz as a useful mean-field description of spin dynamics near the antiferromagnetic $S = 1$ Kitaev limit with weak off-diagonal exchanges.