On the relationship between sigma models and spin chains

Abstract

We consider the two-dimensional $\mathrm{O}(3)$ 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.

arXiv commentTo appear in Int. J. MOd. Phys. B

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• Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators
• Low energy effective Hamiltonian for the XXZ spin chain
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Cited by in corpus (1)

• The Lattice $\beta$-function of Quantum Spin Chains