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Recent numerical studies of the $J_1$-$J_2$ model on a square lattice suggesta possible continuous phase transition between the N\'eel state and a gappedspin-liquid state with Z$_2$ topological order. We show that such a phasetransition can be realized through two steps: First bring the N\'eel state tothe U(1) deconfined quantum critical point, which has been studied in thecontext of N\'eel -- valence bond solid (VBS) state phase transition. Thencondense the spinon pair -- skyrmion/antiskyrmion bound state, which carriesboth gauge charge and flux of the U(1) gauge field emerging at the deconfinedquantum critical point. We also propose a Schwinger boson projective wavefunction to realize such a Z$_2$ spin liquid state and find that it has arelatively low variational energy ($-0.4893J_1$/site) for the $J_1$-$J_2$ modelat $J_2=0.5J_1$. The spin liquid state we obtain breaks the fourfold rotationalsymmetry of the square lattice and therefore is a nematic spin liquid state.This direct continuous phase transition from the N\'eel state to a spin liquidstate may be realized in the $J_1$-$J_2$ model, or the anisotropic$J_{1x}$-$J_{1y}$-$J_2$ model.

Continuous phase transition from N\'eel state to Z_2 spin liquid state on a square lattice