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 , 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 , 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.
 Q. Luo, S. Hu, B. Xi, J. Zhao, and X. Wang, Phys. Rev. B 95 , 165110 (2017).
 Q. Luo, J. Zhao, and X. Wang, arXiv:1910. 01562.