Recently, there has been considerable excitement surrounding the promising realization of high-spin Kitaev material, such as the quasi-2D compound ${\mathrm{CrI}}_3$ and ${\mathrm{CrGeTe}}_3$. However, the stability of quantum spin liquids (QSL) against single-ion anisotropy (SIA) in these materials and the global quantum phase diagram of the extended spin-3/2 Kitaev model with finite SIA remain unclear. In this study, we perform large-scale density matrix renormalization group (DMRG) to explore the quantum phase diagram of the generalized spin-3/2 Kitaev-Heisenberg (K-H) model accompanied with SIA $A_c$. In the $A_c=0$ limit, the spin-3/2 K-H model exhibits a quantum phase diagram similar to that of a spin-1/2 system, including two QSLs around antiferromagnetic and ferromagnetic Kitaev models. For models with finite $A_c$, we map out the quantum phase diagram around two Kitaev points and observe distinct types of in-plane vortex orders developed from these two QSL phases. Interestingly, a series of nearly degenerate vortex configurations is discovered in each vortex phase. Using linear spin-wave theory, we demonstrate that these vortex configurations can be understood as a consequence of the quantum correction on a continuous family of degenerate classical states.

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• Quantum spin liquid
• 2-dimensional systems
• Density matrix renormalization group
• Kitaev model
• Linear spin wave theory