This summer school aims to give an in depth overview of the Bethe ansatz, which is still the only known systematic method to find the ground state properties of non-trivial quantum many-body models. First the models to which the ansatz can be applied will be presented with emphasis on their particular properties, nature of their potentials, and symmetries. The basic coordinate Bethe ansatz will be applied to solve the Heisenberg chain and the Lieb-Liniger gas. Subsequently the nested Bethe-ansatz will be discussed and applied to solve the Hubbard and related models. The extensions of the Bethe ansatz such as the thermodynamics generalization, and the finite size Bethe ansatz methods will also be detailed. The most general approach, namely, the algebraic Bethe ansatz will then be discussed, and finally a set of lectures will be devoted to the general issue of integrability. Also models to which the Bethe ansatz methodology has been applied more recently such as pairing models will be addressed.
The two organizers, Hans-Peter Eckle and Balazs Hetenyi will give service lectures in the beginning of the school. The topics for these service lectures will be chosen after communication with the other lecturers. The other lecturers (expecting 7 lecturers) will be expected to give a basic lecture (3 hrs.), presenting background material to their main research topics, in the days following the service lectures, and a specialized lecture (3 hrs.) which details those research topics in the ending days of the school. They will also be asked to do exercise sessions. Between the basic days of the basic lectures of the lecturers and the days of the specialized lectures there will be a free day, possibly for an excursion.