Exact Haldane mapping for all S and super universality in spin chains

¹  Institute for Theoretical Physics - Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands, EU
²  The Institute of Mathematical Sciences, CIT Campus - Chennai 600 113, India

Corresponding author: shankar@imsc.res.in

Received: 3 January 2008
Accepted: 28 March 2008

Abstract

The low-energy dynamics of the anti-ferromagnetic Heisenberg spin S chain in the semiclassical limit S is known to map onto the nonlinear σ-model with a θ term in 1+1 dimension. Guided by the underlying dual symmetry of the spin chain, as well as by the recently established topological significance of “dangling edge spins”, we report an exact mapping onto the model that avoids the conventional large-S approximation altogether. Our new methodology demonstrates all the super universal features of the θ-angle concept that previously arose in the theory of the quantum Hall effect. It explains why Haldane's original ideas remarkably yield the correct answer in spite of the fundamental complications that generally exist in the idea of semiclassical expansions.