correl24 — Autumn School on Correlated Electrons: Correlations and Phase Transitions

Emergent phenomena are the essence of condensed-matter physics and at the same time what makes the behavior of correlated materials appealing for applications. They are, however, hard to understand at a fundamental level. It is the interplay of several competing interactions — none of which can be treated as a mere perturbation, leading to the emergence of effective interactions — that makes their description a grand challenge. Addressing this problem requires mastery of a wide spectrum of theoretical concepts, ranging from materials modeling using first-principles approaches to advanced many-body methods based on dynamical mean-fields, stochastic simulations and renormalization techniques. The concepts of symmetry, topological invariance and the classification of transitions between phases are of crucial importance to bring order to the plethora of observed phenomena.

The goal of this year’s school is to provide students with an overview of the state-of-the-art in the field of emergent phases in strongly correlated systems and the many techniques used to investigate them. The program will start with fundamental models and concepts, introducing the Hubbard and Anderson Hamiltonians and their physics, and providing an overview of field-theoretical aspects of condensed-matter physics. More advanced lectures will introduce symmetries, Berry phases and topological quantum matter. The focus will then turn to emergent phenomena: superconductivity, conventional and non-conventional, Kondo and heavy-fermion behavior, Kosterlitz-Thouless transitions, Mott phases, orbital-ordering, and quantum phase transitions. The topics will be treated both from the view point of simple models and that of real materials, with an outlook on materials design from the theoretical and experimental viewpoint. The theoretical approaches covered will go from density-functional-theory-based methods to dynamical mean-field theory and quantum Monte Carlo. Experimental lectures will cover phenomena under normal and extreme conditions.

Topics: strong correlations, Mott transition, Kondo physics, quantum magnetism, superconductivity, quantum Monte Carlo, emergent phenomena, dynamical mean-field theory, materials simulations