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We study possible spin liquids on square lattice that respect all latticesymmetries and time-reversal symmetry within the framework of Schwinger boson(mean-field) theory. Such spin liquids have spin gap and emergent Z_2 gaugefield excitations. We classify them by the projective symmetry group method,and find six spin liquid states that are potentially relevant to the J_1-J_2Heisenberg model. The properties of these states are studied under mean-fieldapproximation. Interestingly we find a spin liquid state that can go throughcontinuous phase transitions to either the N\'eel magnetic order or magneticorders of the wavevector at Brillouin zone edge center. We also discuss theconnection between our results and the Abrikosov fermion spin liquids.

Schwinger boson spin liquid states on square lattice