We study possible spin liquids on square lattice that respect all lattice symmetries and time-reversal symmetry within the framework of Schwinger boson (mean-field) theory. Such spin liquids have spin gap and emergent $Z_2$ gauge field excitations. We classify them by the projective symmetry group method, and find six spin-liquid states that are potentially relevant to the $J_1\text{−}{J}_2$ Heisenberg model. The properties of these states are studied under mean-field approximation. Interestingly we find a spin-liquid state that can go through continuous phase transitions to either the Néel magnetic order or magnetic orders of the wave vector at the Brillouin zone edge center. We also discuss the connection between our results and the Abrikosov fermion spin liquids.

• Received 30 July 2015
• Revised 12 May 2016

DOI:https://doi.org/10.1103/PhysRevB.94.035160