Tensor network wave function of S=1 Kitaev spin liquids

The spin-1/2 Kitaev model offers the exactly solvable example of quantum spin liquids. Possible material realizations of the spin-1/2 Kitaev systems and the prospect of using the Majorana fermion excitations for quantum computations have revolutionized quantum spin liquids research. Recently it has been suggested that higher-spin, especially spin-1, Kitaev exchange interactions can be realized in a variety of materials. Numerical computations on small clusters indicate that the ground state of the spin-1 Kitaev model may also be a quantum spin liquid. On the other hand, the nature of the ground state remains elusive since the spin-1 model is not exactly solvable in contrast to the spin-1/2 model. In this work, using the quantum-entanglement based tensor network approach, we construct an explicit ground-state wave function for the spin-1 Kitaev model, which is written only in terms of physical spin operators. We establish the existence of distinct topological sectors on a torus by constructing the minimally entangled states in the degenerate ground-state manifold and evaluating topological entanglement entropy. Our results suggest that the ground state of the spin-1 Kitaev model is a gapped quantum spin liquid with Z2 gauge structure and Abelian quasiparticles. We explain the subtle differences between the spin-1/2 and spin-1 Kitaev quantum spin liquids.