Non-Abelian bosonization and Haldane’s conjecture

Abstract

We study the long-wavelength limit of a spin (Formula presented) Heisenberg antiferromagnetic chain. The fermionic Lagrangian obtained corresponds to a perturbed level (Formula presented) Wess-Zumino-Witten (WZW) model. This effective theory is then mapped into a compact (Formula presented) boson interacting with (Formula presented) parafermions. The analysis of this effective theory allows us to show that when (Formula presented) is an integer there is a mass gap to all excitations, whereas this gap vanishes in the half-odd-integer spin case and the (Formula presented) WZW model flows towards the (Formula presented) stable fixed point. This gives a field theory treatment of the so-called Haldane’s conjecture for arbitrary values of the spin (Formula presented). © 1998 The American Physical Society.