Ground-state and thermodynamic properties of an $S=1$ Kitaev model

We study ground-state and thermodynamic properties of an $S=1$ Kitaev model. We first clarify the existence of global parity symmetry in addition to the local symmetry on each plaquette, which enables us to perform the large scale calculations up to 24 sites. It is found that the ground state should be singlet and its energy is estimated as $E/N\sim -0.65J$, where $J$ is the Kitaev exchange coupling. We find that a lowest excited state belongs to the same subspace as the ground state and the gap monotonically decreases with increasing system size, which suggests that the ground state of the $S=1$ Kitaev model is gapless. By means of the thermal pure quantum states, we clarify finite temperature properties characteristic of the Kitaev models with $S\le 2$.