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Long-range gl(n) integrable spin chains and plane-wave matrix theory
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
2006 (English)In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, no 7, P07006- p.Article in journal (Refereed) Published
Abstract [en]

Quantum spin chains arise naturally from perturbative large-N field theories and matrix models. The Hamiltonian of such a model is a long-range deformation of nearest-neighbor type interactions. Here, we study the most general long-range integrable spin chain with spins transforming in the fundamental representation of gl(n). We derive the Hamiltonian and the corresponding asymptotic Bethe ansatz at the leading four perturbative orders with several free parameters. Furthermore, we propose Bethe equations for all orders and identify the moduli of the integrable system. We finally apply our results to plane-wave matrix theory and show that the Hamiltonian in a closed sector is not of this form and therefore not integrable beyond the first perturbative order. This also implies that the complete model is not integrable.

Place, publisher, year, edition, pages
2006. no 7, P07006- p.
Keyword [en]
Integrable spin chains (vertex models), Quantum integrability (Bethe ansatz)
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-20252DOI: 10.1088/1742-5468/2006/07/P07006ISI: 000239670100020OAI: oai:DiVA.org:uu-20252DiVA: diva2:48025
Available from: 2006-12-06 Created: 2006-12-06 Last updated: 2011-06-27Bibliographically approved

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Klose, Thomas

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