Z2 spin liquids in the S=1/2 Heisenberg model on the kagome lattice: A projective symmetry-group study of Schwinger fermion mean-field states

Due to strong geometric frustration and quantum fluctuation, the S = 1/2 quantum Heisenberg antiferromagnet on the kagome lattice has long been considered as an ideal platform to realize a spin liquid (SL), a phase exhibiting fractionalized excitations without any symmetry breaking. A recent numerical study (Yan et al., e-print arXiv: 1011.6114) of the Heisenberg S = 1/2, kagome lattice model (HKLM) shows, in contrast to earlier results, that the ground state is a singlet-gapped SL with signatures of Z(2) topological order. Motivated by this numerical discovery, we use the projective symmetry group to classify all 20 possible Schwinger fermion mean-field states of Z(2) SLs on the kagome lattice. Among them we found only one gapped Z(2) SL (which we call the Z(2)[0,pi]beta state) in the neighborhood of the U(1) Dirac SL state. Since its parent state, i.e., the U(1) Dirac SL, was found [Ran et al., Phys. Rev. Lett. 98, 117205 (2007)] to be the lowest among many other candidate U(1) SLs, including the uniform resonating-valence-bond states, we propose this Z(2)[0,pi]beta state to be the numerically discovered SL ground state of the HKLM.