Stability of three-sublattice order in S=1 bilinear-biquadratic Heisenberg Model on anisotropic triangular lattices

The S=1 bilinear-biquadratic Heisenberg model on anisotropic triangular lattices is investigated by several complementary methods. Our focus is on the stability of the three-sublattice spin nematic state against spatial anisotropy. We find that, deviated from the case of isotropic triangular lattice, quantum fluctuations enhance and the three-sublattice spin nematic order is reduced. In the limit of weakly coupling chains, by mapping the systems to an effective one-dimensional model, we show that the three-sublattice spin nematic order develops at infinitesimal interchain coupling. Our results provide a complete picture for smooth crossover from the triangular-lattice case to both the square-lattice and the one-dimensional limits.