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On the relationship between sigma models and spin chains

D. Controzzi·E. Hawkins
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Abstract

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 $θ$ of the topological term is quantized as $θ=2πs$, 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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D. Controzzi, E. Hawkins. 2005-09-06. On the relationship between sigma models and spin chains. https://doi.org/10.1142/s0217979205032826

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