Continuous phase transition from Néel state to Z2 spin-liquid state on a square lattice

Recent numerical studies of the J1-J2 model on a square lattice suggest a possible continuous phase transition between the Néel state and a gapped spin-liquid state with Z2 topological order. We show that such a phase transition can be realized through two steps: First bring the Néel state to the U(1) deconfined quantum critical point, which has been studied in the context of Néel–valence bond solid (VBS) state phase transition. Then condense the spinon pair–skyrmion/antiskyrmion bound state, which carries both gauge charge and flux of the U(1) gauge field emerging at the deconfined quantum critical point. We also propose a Schwinger boson projective wave function to realize such a Z2 spin liquid state and find that it has a relatively low variational energy (−0.4893J1/site) for the J1-J2 model at J2 = 0.5J1. The spin liquid state we obtain breaks the fourfold rotational symmetry of the square lattice and therefore is a nematic spin liquid state. This direct continuous phase transition from the Néel state to a spin liquid state may be realized in the J1-J2 model, or the anisotropic J1x-J1y-J2 model.