We investigate the quantum spin liquid (QSL) ground state of anisotropic Kitaev model with antiferromagnetic (AFM) coupling under the $[001]$ magnetic field with the finite-temperature Lanczos method (FTLM). In this anisotropic AFM Kitaev model with $K_{X}=K_{Y}$, $K_{X}+K_{Y}+K_{Z}=-3K$, and $K_{Z}<-K$, with magnetic field increasing, the gapped QSL experiences a transition to a gapless QSL at $h_{c1}=gmu_{B}H_{z1}/K$, to another gapless QSL with $C_{6}$ rotational symmetry at $h_{c2}$, and to a new $U(1)$ gapless QSL between $h_{c3}$ and $h_{c4}$, respectively. These indicate that magnetic field could first turn the anisotropic gapped or gapless QSL back into the isotropic $C_{6}$ gapless one and then make it to undergo the similar evolution as the isotropic case. Moreover, the critical magnetic fields $h_{c1}$, $h_{c2}$, $h_{c3}$, and $h_{c4}$ come up monotonically with the increasing Kitaev coupling; this suggests that the magnetic field can be applied to the modulation of the anisotropic Kitaev materials.
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