Spin-liquid states on the triangular and Kagome lattices: A projective-symmetry-group analysis of Schwinger boson states

A symmetry-based analysis (projective symmetry group) is used to study spin-liquid phases on the triangular and Kagome lattices in the Schwinger boson framework. A maximum of eight distinct Z(2) spin-liquid states are found for each lattice, which preserve all symmetries. Out of these only a few have nonvanishing nearest-neighbor amplitudes, which are studied in greater detail. On the triangular lattice, only two such states are present-the first (zero-flux state) is the well-known state introduced by Sachdev, which on condensation of spinons leads to the 120 degrees ordered state. The other solution, which we call the pi-flux state has not previously been discussed. Spinon condensation leads to an ordering wave vector at the Brillouin zone edge centers, in contrast to the 120 degrees state. While the zero-flux state is more stable with just nearest-neighbor exchange, we find that the introduction of either next-neighbor antiferromagnetic exchange or four-spin ring exchange (of the sign obtained from a Hubbard model) tends to favor the pi-flux state. On the Kagome lattice four solutions are obtained-two have been previously discussed by Sachdev, which on spinon condensation give rise to the q=0 root 3x root 3 spin-ordered states. In addition we find two states with significantly larger values of the quantum parameter at which magnetic ordering occurs. For one of them this even exceeds unity kappa(c)approximate to 2.0 in a nearest-neighbor model, indicating that if stabilized, could remain spin disordered for physical values of the spin. This state is also stabilized by ring-exchange interactions with signs as derived from the Hubbard model.