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Recently, it has been proposed that higher-spin analogues of the Kitaevinteractions $K>0$ may also occur in a number of materials with strong Hund'sand spin-orbit coupling. In this work, we use Lanczos diagonalization anddensity matrix renormalization group methods to investigate numerically the$S=1$ Kitaev-Heisenberg model. The ground-state phase diagram and quantum phasetransitions are investigated by employing local and nonlocal spin correlations.We identified two ordered phases at negative Heisenberg coupling $J<0$:a~ferromagnetic phase with $\langle S_i^zS_{i+1}^z\rangle>0$ and anintermediate left-left-right-right phase with $\langleS_i^xS_{i+1}^x\rangle\neq 0$. A~quantum spin liquid is stable near the Kitaevlimit, while a topological Haldane phase is found for $J>0$.

Quantum phase transitions in the spin-1 Kitaev-Heisenberg chain