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Material realizations of the bond-dependent Kitaev interactions with $S$=1/2local moments have vitalized the research in quantum spin liquids. Recently, ithas been proposed that higher-spin analogues of the Kitaev interactions mayalso occur in a number of materials with strong spin-orbit coupling. Incontrast to the celebrated $S$=1/2 Kitaev model on the honeycomb lattice, thehigher-spin Kitaev models are not exactly solvable. Hence, the existence ofquantum spin liquids in these systems remains an outstanding question. In thiswork, we use the density matrix renormalization group (DMRG) methods tonumerically investigate the $S$=1 Kitaev model with both ferromagnetic (FM) andantiferromagnetic (AFM) interactions. Using results on a cylindrical geometrywith various circumferences, we conclude that the ground state of the $S$=1Kitaev model is a quantum spin liquid with a $\mathbb{Z}_2$ gauge structure. Wealso put a bound on the excitation gap, which turns out to be quite small. Themagnetic field responses for the FM and AFM models are similar to those of the$S$=1/2 counterparts. In particular, in the AFM $S$=1 model, a gapless quantumliquid state emerges in an intermediate window of magnetic field strength,before the system enters a trivial polarized state.

Characterizing spin-one Kitaev quantum spin liquids