Probable absence of a quadrupolar spin-nematic phase in the   bilinear-biquadratic spin-1 chain
  We study numerically the ground-state phase diagram of the bilinear-biquadratic spin-1 chain near the ferromagnetic instability point, where the existence of a gapped or gapless nondimerized quantum nematic phase has been suggested. Our results, obtained by a highly accurate density-matrix renormalization-group (DMRG) calculation are consistent with the view that the order parameter characterizing the dimer phase vanishes only at the point where the system becomes ferromagnetic, although the existence of a gapped or gapless nondimerized phase in a very narrow parameter range between the ferromagnetic and the dimerized regimes cannot be ruled out. 
K. Buchta, G. F\'ath, \"O. Legeza, and J. S\'olyom