  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 charge anyon excitation. Bottom
of the gapped single-particle charge excitations are found at $\mathbf{K},
\mathbf{K}'=(\pm2\pi/3, \mp 2\pi/3)$, 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

Strongly Correlated Electrons