Non-Abelian bosonization and Haldane's conjecture

We study the long-wavelength limit of a spin S Heisenberg antiferromagnetic chain. The fermionic Lagrangian obtained corresponds to a perturbed level 2S SU(2) Wess-Zumino-Witten (WZW) model. This effective theory is then mapped into a compact U(1) boson interacting with Z(2s) parafermions. The analysis of this effective theory allows us to show that when S is an integer there is a mass gap to all excitations, whereas this gap vanishes in the half-odd-integer spin case and the SU(2)(2s) WZW model flows towards the SU(2)1 stable fixed point. This gives a field theory treatment of the so-called Haldane's conjecture for arbitrary values of the spin S. [S0163-1829(98)04726-2].