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arXiv · hep-th/9802014

Non-Abelian Bosonization and Haldane's Conjecture

D. C. Cabra·P. Pujol·C. von Reichenbach
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Abstract

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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D. C. Cabra, P. Pujol, C. von Reichenbach. 1998-02-03. Non-Abelian Bosonization and Haldane's Conjecture. https://doi.org/10.1103/physrevb.58.65

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