Exact and Numerical Models of Low-Dimensional Quantum Structures

The aim of this summer school is to bring together researchers who study low-dimensional systems. Particular emphasis will be placed on integrable systems and the Bethe ansatz, but to broaden the scope of the school a set of lectures on related topics, the Luttinger liquids and the density matrix renormalization group will also be included. Basic lectures will present the coordinate Bethe ansatz, applied to fundamental models such as the Lieb-Liniger gas, XXZ Heisenberg , Kondo , Yang-Gaudin, and Hubbard models. A discussion of the relation between two-dimensional classical vertex models and the basis of the algebraic Bethe ansatz will follow. Lectures will also cover the application of the Bethe ansatz to a range of topics of recent interest, such as the Tavis-Cummings model used in quantum optics, the Richardson-Gaudin model applied to mesoscopic systems, systems far from equilibrium, quantum quench dynamics, and magnetism of cold bosons. All lectures will be followed by an exercise session.