EXTENDED MASSLESS PHASE AND THE HALDANE PHASE IN A SPIN-1 ISOTROPIC ANTIFERROMAGNETIC CHAIN

We study the phase diagram of isotropic spin-1 models in the vicinity of the Uimin-Lai-Sutherland (ULS) model. This is done with the help of a level-one SU(3) Wess-Zumino-Witten model with certain marginal pert urbations. We find that the renormalization-group flow has infrared st able and unstable trajectories divided by a critical line on which the ULS model is located. The infrared unstable trajectory produced by a marginally relevant perturbation generates an exponential mass gap for the Haldane phase, and thus the universality class of the transition from the massless phase to the Haldane phase at the ULS point is ident ified with the Berezinskii-Kosterlitz-Thouless type. Our results suppo rt recent numerical studies by Fath and Solyom. In the massless phase, we calculate logarithmic finite-size corrections of the energy for th e SU(nu)-symmetric and asymmetric models in the massless phase.