Generalization of the Haldane conjecture to SU(3) chains

We apply field theory methods to SU(3) chains in the symmetric representation, with p boxes in the Young tableau, mapping them into a flag manifold nonlinear σ-model with a topological angle θ=2πp/3. Generalizing the Haldane conjecture, we argue that the models are gapped for p=3m but gapless for p=3m±1 (for integer m), corresponding to a massless phase of the σ-model at θ=±2π/3. We confirm this with Monte Carlo calculations on the σ-model.