Overview

This summer school aims to provide an in-depth overview of the low-dimensional
systems with a particular, but not exclusive, emphasis on the Bethe ansatz. The Bethe ansatz solution
of certain one-dimensional models is still the only known systematic method to find the ground state
properties of non-trivial quantum many-body models. While some lectures will be basic and
pedagogical, focusing on the models (Hubbard, Heisenberg, Lieb-Liniger models), and the methods
(coordinate Bethe ansatz, algebraic Bethe ansatz, nested Bethe ansatz, thermodynamics Bethe
ansatz, finite size Bethe ansatz), but more advanced topics will also be covered, such as transport,
properties, correlation functions, non-equilibrium phenomena, quantum quenches, quantum
entanglement and the general issue of quantum integrability. These topics serve as a guideline to the
school, but they will be replaced by more specifics when the program based on the actualy abstracts of
the lecturers are considered.

References for banner photos:

• M T Batchelor, H W J Blöte, B Nienhuis and C M Yung, J. Phys. A: Math. Gen. 29 No 16 (21 August 1996) L399-L404
• I. Gilbert, U. of I.