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Yangian Symmetry of Long-Range gl(N) Integrable Spin Chains

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Beisert,  Niklas
Duality & Integrable Structures, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Beisert, N., & Erkal, D. (2008). Yangian Symmetry of Long-Range gl(N) Integrable Spin Chains. Journal of Statistical Mechanics: Theory and Experiment, 08: P03001. doi:10.1088/1742-5468/2008/03/P03001.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-6264-E
Abstract
An interesting type of spin chain has appeared in the context of the planar AdS/CFT correspondence: It is based on an integrable nearest-neighbor spin chain, and it is perturbatively deformed by long-range interactions which apparently preserve the integrable structure. Similar models can be constructed by demanding the existence of merely one conserved local charge. Although the latter is not a sufficient integrability condition in general, the models often display convincing signs of full integrability. Here we consider a class of long-range spin chains with spins transforming in the fundamental representation of gl(N). For the most general such model with one conserved local charge we construct a conserved Yangian generator and show that it obeys the Serre relations. We thus provide a formal proof of integrability for this class of models.