The Geometry of Antiferromagnetic Spin Chains
2013 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 322, no 3, 807-834 p.Article in journal (Refereed) Published
It has been a conjecture of F.D.M.Haldane that long-wavelength excitations around antiferromagnetic vacua of certain spin chains are related to relativistic two-dimensional sigma-models. We construct a class of such spin chains and associated sigma-models, using symplectic geometry as a main tool. The target space of the sigma-model can be an arbitrary complex flag manifold, and we find universal expressions for the metric and theta-term. The derivation relies on the fact that the flag manifold is a Lagrangian submanifold in a direct product of Grassmannians associated (via geometric quantization) to the representations of spins at consecutive sites of the spin chain.<BlockQuote> <Para>The true goal is not to reach the uttermost limits, but to discover a completeness that knows no boundaries. Rabindranath Tagore.
Place, publisher, year, edition, pages
2013. Vol. 322, no 3, 807-834 p.
Mathematics Physical Sciences
IdentifiersURN: urn:nbn:se:su:diva-92788DOI: 10.1007/s00220-013-1702-5ISI: 000321957000005OAI: oai:DiVA.org:su-92788DiVA: diva2:642794
RFBR: 11-01-00296-a, 11-01-12037-ofi-m-201, 12-01-31298-mol-a; Support of Leading Scientific Schools of Russia NSh-4612.2012.1. 2013-08-232013-08-202013-08-23Bibliographically approved