Haldane limits via Lagrangian embeddings

Details Haldane limits via Lagrangian embeddings Haldane limits via Lagrangian embeddings

2011-04-07

arxiv.org/abs/1104.1419v1

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, 2 figures

Scientific paper

In the present paper we revisit the so-called Haldane limit, i.e. a particular continuum limit, which leads from a spin chain to a sigma model. We use the coherent state formulation of the path integral to reduce the problem to a semiclassical one, which leads us to the observation that the Haldane limit is closely related to a Lagrangian embedding into the classical phase space of the spin chain. Using this property, we find a spin chain whose limit produces a relativistic sigma model with target space the manifold of complete flags U(N)/U(1)^N. We discuss possible other future applications of Lagrangian/isotropic embeddings in this context.

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