Séminaire de Physique ThéoriqueBethe ansatz for Gaudin models without proper pseudo vacuum
Alexandre Faribault (Université de Lorraine)
Thursday 22 June 2017 14:00 - Tours - Salle 1180 (Bât E2)
This work deals with the rational family of Gaudin models. We show how, in certain scenarios, one can build a Bethe ansatz solution from purely algebraic considerations even when the realisation of the underlying Generalised Gaudin algebra is such that it does not allow for a proper pseudovacuum, eigenstate of the transfer matrix, to be built. A dual representation for spin-boson models as well a common framework for XXX central spin models in arbitrarily oriented magnetic fields, are obtained in a similar fashion. The resulting constructions can then give access to determinant expressions for certain scalar products.