An extended massless phase and the Haldane phase in a spin-1 isotropic antiferromagnetic chain

TL;DR

This paper investigates the phase transition in spin-1 isotropic antiferromagnetic chains near the Uimin-Lai-Sutherland point, revealing a BKT transition and characterizing the massless and Haldane phases using conformal field theory.

Contribution

It introduces an analysis of the phase transition using SU(3)_1 WZW models with marginal perturbations, providing a theoretical framework for the massless and Haldane phases.

Findings

The transition from massless to Haldane phase is of BKT type.

Marginal perturbations generate a mass gap in the Haldane phase.

Logarithmic finite-size corrections are calculated for SU(ν) models.

Abstract

We study the phase transition of isotropic spin-1 models in the vicinity of the Uimin-Lai-Sutherland model by using the SU(3)_1 WZW model with certain marginal perturbations. The unstable RG trajectory by a marginally relevant perturbation generates a mass gap for the Haldane phase, and thus the universality class of the transition from the massless phase to the Haldane phase at ULS point becomes the BKT type. Our results support recent numerical studies by F\'ath and S\'olyom. In the massless phase, we calculate logarithmic finite-size corrections of the energy for the SU(\nu)-symmetric and asymmetric models.