The Elliptic Gaudin Model

Trento, September, 21-25 September, 2015The Richardson-Gaudin integrable models have been widely applied in recent years to a large variety of mesoscopic systems, like quantum dots, small grains, atomic nuclei, cold atoms, etc. Moreover, particular realizations of the RG models lead to models with ESQPT's like Likin, Tavis-Cummings, two-level pairing, and IBM. Here we will introduce the yet unexplored EGM showing the kind of spin systems it can describe. In particular, we will present an EGM consisting of a spin 1/2 interacting with a large spin J. This model, which is a schematic realization of the anisotropic central spin model, contains two ESQPTs that we will describe in detail.Peer Reviewe