Volume 82, Number 4, May 2008
Article Number 47005
Number of page(s) 5
Section Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties
Published online 08 May 2008
EPL, 82 (2008) 47005
DOI: 10.1209/0295-5075/82/47005

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

A. M. M. Pruisken1, R. Shankar2 and N. Surendran1

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

received 3 January 2008; accepted in final form 28 March 2008; published May 2008
published online 8 May 2008

The low-energy dynamics of the anti-ferromagnetic Heisenberg spin S chain in the semiclassical limit S $\rightarrow\infty$ is known to map onto the O(3) nonlinear $\sigma$-model with a $\theta$ 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 O(3) model that avoids the conventional large-S approximation altogether. Our new methodology demonstrates all the super universal features of the $\theta$-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.

73.43.Cd - Quantum Hall effects: Theory and modeling.
75.10.Jm - Quantized spin models.
11.10.Kk - Field theories in dimensions other than four.

© EPLA 2008