We study the excitation spectrum of the spin-1 Kitaev model using the symmetric tensor network. By evaluating the virtual order parameters defined on the virtual Hilbert space in the tensor network formalism, we confirm the ground state is in a ${\mathbb{Z}}_2$ spin-liquid phase. Using the correspondence between the transfer matrix spectrum and low-lying excitations, we find that contrary to the dispersive Majorana excitation in the spin-1/2 case, the isotropic spin-1 Kitaev model has a dispersive bosonic charge excitation. The bottom of the gapped single-particle charge excitations is found at $\mathbf{K},{\mathbf{K}}^{\prime }=(\pm 2\pi /3,\mp 2\pi /3)$, with a corresponding correlation length of $\xi \approx 6.7$ unit cells. The lower edge of the two-particle continuum, which is closely related to the dynamical structure factor measured in inelastic neutron scattering experiments, is obtained by extracting the excitations in the vacuum superselection sector in the anyon theory language.

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• Quantum spin liquid
• Topological materials
• Kitaev model
• Tensor network methods
• Tensor network renormalization