Séminaire de Physique ThéoriqueNested Bethe ansatz and open spin chains
Samuel Belliard (Annecy, LAPTH)
Friday 03 April 2009 14:00 - Tours - Salle 1180 (Bât E2)
Periodic spin chains introduced by Heisenberg are fundamental models in the elaboration of quantum integrability. The simplest model, XXX, has been solved in 1935 by Bethe with the use of a method now called "Bethe Ansatz". This method has then been improved by the Leningrad school during the eighties and has led to the discovery of Quantum Algebras. In 1983 Sklyanin has introduced new algebras related to the open spin chains (with boundary conditions) for sl(2) type quantum algebras. I will present the outline of the Nested Bethe Ansatz (introduced by Reshetikin and Kulish in 1981 for periodic case) for open spin chains of gl(n)-Yangians type. I will discuss the allowed boundary conditions for the validity of this method and open problems from this result. This is a part of a work done with Eric Ragoucy in arxiv: [math-ph] 0902.0321.