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

TL;DR

This paper proves the integrability of a class of long-range gl(N) spin chains by constructing a Yangian symmetry generator that satisfies the Serre relations, extending understanding of integrable models in AdS/CFT contexts.

Contribution

It constructs a Yangian symmetry generator for long-range gl(N) spin chains with one conserved charge, formally proving their integrability.

Findings

Constructed a Yangian generator satisfying Serre relations.

Provided formal proof of integrability for the class of models.

Extended the understanding of symmetries in long-range spin chains.

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.