Haldane limits via Lagrangian embeddings

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 Lagrarwian 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(3)/U(1)(3). We discuss possible other future applications of Lagrangian/isotropic embeddings in this context. (C) 2011 Elsevier B.V. All rights reserved.