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Projective symmetry groups (PSG) are the mathematical tools which allow tolist and classify mean-field spin liquids (SL) based on a parton construction.The seminal work of Wen and its subsequent extension to bosons by Wang andVishwanath concerned the so-called symmetric SL: i.e. states that break neitherlattice symmetries nor time reversal invariance. Here we generalize thisapproach to chiral (time reversal symmetry breaking) SL described in aSchwinger boson mean-field approach. A special emphasis is put on frustratedlattices (triangular and kagome lattices), where the possibility of a chiral SLground state has recently been discussed. The PSG approach is detailed for thetriangular lattice case. Results for other lattices are given in theappendices. The physical significance of gauge invariant quantities calledfluxes is discussed both in the classical limit and in the quantum SL and theirexpressions in terms of spin observables are given.

Time-reversal-symmetry-breaking chiral spin liquids: a projective symmetry group approach of bosonic mean-field theories