Autumn School on Correlated Electrons: Dynamical Mean-Field Theory of Correlated Electrons

Correlated systems are characterized by strong electron-electron interactions, resulting in many-body effects eluding a static mean-field description. They thus proved largely intractable until the development of dynamical mean-field theory (DMFT). In this approach, mapping the lattice onto an auxiliary impurity problem gives a local dynamical self-energy, which captures the essence of electronic correlations. DMFT is exact in the limit of infinite dimensions, and often provides an excellent approximation for real crystal structures. This crucial insight represented a paradigm shift in the study of correlations. Solving ever more complex impurity problems nowadays allows the simulation of real materials, making contact with experiment via the calculation of spectra, dynamical response functions, and non-equilibrium properties. Even subtle non-local effects can be captured using various approaches, including clusters of impurities or diagrammatic expansions. Thus DMFT finds application not only in correlated bulk systems but also in heterostructures, and can even be employed to understand the properties of topological phases of strongly correlated electron systems.

This year's school will introduce the concept of dynamical mean fields and explore how it can be used to understand the physics of real materials. Lectures will range from Fermi liquids and the limit of infinite dimensions to the physics of quantum impurities and their relation to the properties of correlated lattice systems.

The goal of the school is to introduce advanced graduate students and up to this modern method for the realistic modeling of strongly correlated matter.

Topics: correlated systems, dynamical mean field theory, Fermi liquid, Mott transition, machine leaning, quantum impurities, out of equilibrium phenomena, topological phases, non-local effects, heterostructures, superconductivity