Quantum phase diagram of the extended Spin-3/2 Kitaev Heisenberg model on three- and four-leg cylinders

Recently there has been considerable excitement surrounding the promising realization of high-spin Kitaev material, such as the quasi-2D compound CrI₃ and CrGeTe₃. However, the stability of quantum spin liquids (QSL) against the extra single ion anisotropy (SIA) in these high-spin materials and the global quantum phase diagram of the extended Kitaev model with SIA term remains still unclear. In this work, we perform large-scale density matrix renormalization group to explore the quantum phase diagram of the generalized spin-3/2 Kitaev-Heisenberg (K-H) model accompanied with the SIA interaction A_c. In the A_c=0 limit, the spin-3/2 K-H model exhibits a similar quantum phase diagram as the one of the spin-1/2 system, including two QSLs around antiferromagnetic and ferromagnetic Kitaev models. As the SIA interaction increases, we find that the QSL in the AFM Kitaev model is fragile against the SIA interaction and a first order phase transition between QSL and AFM ordered phase happens at A_c ∼ 0.05. While for the FM Kitaev model, a new magnetic ordered phase emerges through a continuous phase transition at A_c ∼ 0.04. The effect of the SIA term on other magnetic ordered phases is also discussed.