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Haldane limits via Lagrangian embeddings

By Dmitri Bykov

Abstract

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.Comment: 29 pages, 2 figure

Topics: High Energy Physics - Theory, Condensed Matter - Strongly Correlated Electrons
Year: 2011
DOI identifier: 10.1016/j.nuclphysb.2011.10.005
OAI identifier: oai:arXiv.org:1104.1419
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