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

• Received 20 August 2020
• Accepted 28 September 2020

DOI:https://doi.org/10.1103/PhysRevB.102.144437

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society