Spin-Wave Theory of the Multiple-Spin Exchange Model on a Triangular   Lattice in a Magnetic Field : 3-Sublattice Structures
  We study the spin wave in the S=1/2 multiple-spin exchange model on a triangular lattice in a magnetic field within the linear spin-wave theory. We take only two-, three- and four-spin exchange interactions into account and restrict ourselves to the region where a coplanar three-sublattice state is the mean-field ground state. We found that the Y-shape ground state survives quantum fluctuations and the phase transition to a phase with a 6-sublattice structure occurs with softening of the spin wave. We estimated the quantum corrections to the ground state sublattice magnetizations due to zero-point spin-wave fluctuations. 
Chitoshi Yasuda, Daisuke Kinouchi and Kenn Kubo