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

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

2008-01-03

arxiv.org/abs/0801.0511v1

Europhys. Lett. 82, 47005 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Scientific paper

10.1209/0295-5075/82/47005

The low energy dynamics of the anti-ferromagnetic Heisenberg spin $S$ chain in the semiclassical limit $S\to\infty$ 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 the recently established topological significance of "dangling edge spins," we report an {\em 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.

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