Material realizations of the bond-dependent Kitaev interactions with $S=1/2$ local moments have vitalized the research in quantum spin liquids. Recently, it has been proposed that higher-spin analogs of the Kitaev interactions may also occur in a number of materials with strong spin-orbit coupling. In contrast to the celebrated $S=1/2$ Kitaev model on the honeycomb lattice, the higher-spin Kitaev models are not exactly solvable. Hence, the existence of quantum spin liquids in these systems remains an outstanding question. In this paper, we use the density matrix renormalization group methods to numerically investigate the $S=1$ Kitaev model with both ferromagnetic (FM) and antiferromagnetic (AFM) interactions. Using results on quasi-one-dimensional finite-size cylindrical geometries with circumferences of up to six legs, we conclude that the ground state of the $S=1$ Kitaev model is a quantum spin liquid with a ${\mathbb{Z}}_2$ gauge structure. We are also able to put an upper bound on the excitation gap. The magnetic 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 quantum spin-liquid state emerges in an intermediate window of magnetic field strength, before the system enters a trivial polarized state.

• Received 6 February 2020
• Accepted 31 January 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.013160

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Published by the American Physical Society