2007/11/30 by Niklas Beisert, Denis Erkal
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum many-body systems #hep-th
paper · pdf · doi:10.1088/1742-5468/2008/03/p03001
published as J.Stat.Mech.0803:P03001,2008 · 27 pages, v2: minor changes, references added, figures updated, v3: minor corrections, references added, to appear in JSTAT
arxiv created 2008/02/28 · openalex publication_date 2008/03/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 . 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.