Classifying Nearest-Neighbor Interactions and Deformations of AdS
Marius de Leeuw, Chiara Paletta, Anton Pribytok, Ana L. Retore, Paul Ryan
Abstract
We classify all regular solutions of the Yang-Baxter equation of eight-vertex type. Regular solutions correspond to spin chains with nearest-neighbor interactions. We find a total of four independent solutions. Two are related to the usual six- and eight-vertex models that have R matrices of difference form. We find two new solutions of the Yang-Baxter equation, which are manifestly of nondifference form. These new solutions contain the S-matrices of the AdS_{2} and AdS_{3} integrable models as a special case. This can be used as a starting point to study and classify integrable deformations of these holographic integrable systems.
Topics & Concepts
Integrable systemVertex (graph theory)Mathematical physicsVertex modelType (biology)PhysicsSpin (aerodynamics)k-nearest neighbors algorithmYang–Baxter equationPure mathematicsMathematicsCombinatoricsQuantum mechanicsComputer scienceQuantumGraphThermodynamicsEcologyArtificial intelligenceBiologyAlgebraic structures and combinatorial modelsNonlinear Waves and SolitonsBlack Holes and Theoretical Physics