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  Long-range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory

Beisert, N., & Klose, T. (2006). Long-range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory. Journal of Statistical Mechanics: Theory and Experiment, P07006. Retrieved from http://www.iop.org/EJ/abstract/1742-5468/2006/07/P07006.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4B59-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4B5B-9
Genre: Journal Article

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jstat6_07_p07006.pdf (Publisher version), 794KB
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 Creators:
Beisert, Niklas1, Author              
Klose, Thomas2, Author
Affiliations:
1Duality & Integrable Structures, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24016              
2Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              

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 Abstract: 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.

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 Dates: 2006
 Publication Status: Published in print
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Title: Journal of Statistical Mechanics: Theory and Experiment
Source Genre: Journal
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Publ. Info: Bristol, England : Institute of Physics Publishing
Pages: - Volume / Issue: - Sequence Number: P07006 Start / End Page: - Identifier: Other: 111076098244006
Other: 1742-5468