From Neel long-range order to spin liquids in the multiple-spin exchange model

The phase diagram of the multiple-spin exchange model on the triangular lattice is studied using exact diagonalizations. The two-spin (J(2)) and four-spin (J(4)) exchanges have been taken into account for 12-, 16-, 19-, 21-, 24-, and 27-site samples in the parameter region J(4)=0-0.25 (for a fixed J(2)=1) ft is found that the three-sublattice Neel-ordered state built up by the pure two-spin exchange can be destroyed by the four-spin exchange, forming a spin-liquid state. The different data suggest that the phase diagram in this range of parameters exhibits two phases. The pure J(2) phase is a three-sublattice Neel-ordered phase; a small J(4) drives it into a spin-liquid state with a spin gap filled of a large number of singlets. This spin-liquid phase is not of the Same generic kind as the phase studied by Misguich et al. [Phys. Rev. B 60, 1064 (1999)]. It is observed on the finite-size samples that the spin-liquid phase, as the Neel-ordered phase, exhibits a magnetization plateau at m=1/3, and for J(4)>0.15 a second plateau at m=1/2. These two plateaus are associated, respectively, with the semiclassical orderings uud and uuud.