The quantum spin liquid (QSL) is an exotic phase and it is a challenging task for theorists to reveal its nature in real materials. In this talk, I will present my recent works by density-matrix renormalization group method on two spin-orbit coupled models, in connection with the QSL candidates YbMgGaO$_4$ and $alpha$-RuCl$_3$. In the former work [1], we fail to detect the trail of QSL in the trial mimic model [Y. Li et al., Phys. Rev. Lett. 115 , 167203 (2015)], instead, find three magnetically ordered phases, i.e., the 120° phase, the stripe-A and stripe-B phases. Interestingly, in contrast to the classical counterpart, we rule out the possibility of first-order transition between the two stripe phases. In the latter work [2], we address the issue concerning the nature of the ground state of the honeycomb Γ antiferromagnet (HCΓA). To this end, we propose a novel model by introducing a bond-modulated Heisenberg interaction in addition to the Γ-term. We figure out a gapless QSL phase sandwiched between two magnetically ordered phases in the phase diagram and affirm that the ground state of HCΓA belongs to it.

[1] Q. Luo, S. Hu, B. Xi, J. Zhao, and X. Wang, Phys. Rev. B 95 , 165110 (2017).

[2] Q. Luo, J. Zhao, and X. Wang, arXiv:1910. 01562.