On the relationship between sigma models and spin chains

Details On the relationship between sigma models and spin chains On the relationship between sigma models and spin chains

2005-09-06

arxiv.org/abs/cond-mat/0509140v1

Int.J.Mod.Phys. B19 (2005) 4449-4466

Physics

Condensed Matter

Strongly Correlated Electrons

To appear in Int. J. MOd. Phys. B

Scientific paper

10.1142/S0217979205032826

We consider the two-dimensional $\rm O(3)$ non-linear sigma model with topological term using a lattice regularization introduced by Shankar and Read [Nucl.Phys. B336 (1990), 457], that is suitable for studying the strong coupling regime. When this lattice model is quantized, the coefficient $\theta$ of the topological term is quantized as $\theta=2\pi s$, with $s$ integer or half-integer. We study in detail the relationship between the low energy behaviour of this theory and the one-dimensional spin-$s$ Heisenberg model. We generalize the analysis to sigma models with other symmetries.

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