• DOI:10.1103/PhysRevB.74.174423
• Corpus ID: 119510610

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

@article{Wang2006SpinliquidSO,
  title={Spin-liquid states on the triangular and Kagom{\'e} lattices: A projective-symmetry-group analysis of Schwinger boson states},
  author={Fa Wang and Ashvin Vishwanath},
  journal={Physical Review B},
  year={2006},
  volume={74},
  pages={174423}
}

• Fa Wang, A. Vishwanath
• Published 4 August 2006
• Physics
• Physical Review B

A symmetry-based analysis (projective symmetry group) is used to study spin-liquid phases on the triangular and Kagom\'e 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\ifmmode^\circ\else\textdegree\fi{} ordered state. The other solution, which we call the $\ensuremath{\pi}$-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\ifmmode^\circ\else\textdegree\fi{} 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 $\ensuremath{\pi}$-flux state. On the Kagom\'e lattice four solutions are obtained---two have been previously discussed by Sachdev, which on spinon condensation give rise to the $q=0$ and $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ 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 ${\ensuremath{\kappa}}_{c}\ensuremath{\approx}2.0$ 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.