Non-Abelian Bosonization and Haldane's Conjecture

Details Non-Abelian Bosonization and Haldane's Conjecture Non-Abelian Bosonization and Haldane's Conjecture

1998-02-03

arxiv.org/abs/hep-th/9802014v1

Phys.Rev. B58 (1998) 65-68

Physics

High Energy Physics

High Energy Physics - Theory

9 pages REVTeX, no figures

Scientific paper

10.1103/PhysRevB.58.65

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 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. This gives a field theory treatment of the so-called Haldane's conjecture for arbitrary values of the spin S.

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