Many-body physics: from Kondo to Hubbard

Many-body physics has the daunting task of describing the collective behavior of vast assemblies of elementary objects. While the fundamental laws are known, exact solutions like the Bethe Ansatz are exceedingly rare. Nonetheless, the past century has witnessed a continuous stream of conceptual breakthroughs, prompted by unforeseen discoveries of new states of matter: superconductivity and superfluidity, antiferromagnetism, the Kondo effect, the Mott transition, symmetry breaking, spin glasses and frustration, heavy Fermions, and high-temperature superconductivity. Each of these cooperative phenomena is an example of emergence at work. Their essence can often be captured by simple model Hamiltonians. Describing the richness of real matter requires, however, to increase the complexity of the models significantly, as emergent phenomena are frequently governed by the interplay of several scales. In this year’s school we will highlight the Kondo effect, the physics of the Hubbard model, and frustrated quantum spins, covering the range from fundamental mechanisms to the modeling of real materials. The aim of the school is to introduce advanced graduate students and up to the essence of emergence and modern approaches for modeling strongly correlated matter