Autumn School on Correlated Electrons: Methods and Applications

Scope

Solving the many-electron problem is the grand challenge of condensed-matter physics. Interacting electrons in fact lose their individuality forming emergent co-operative states, whose nature is difficult to unravel. Progress in understanding correlated states of matter requires the combination of several complementary approaches, theoretical and experimental. Only in this way on can pinpoint the microscopic mechanisms driving the co-operative phenomena characterizing strongly-correlated systems.The goal of this year’s school is to provide students with an overview of modern many-body methods and their application to materials, with an outlook to the future of many-body simulations. The program will start with introducing the fundamentals: density-functional theory, the many-body problem and its complexity, emergent phenomena, the Hubbard and Kondo models and their physics. More advanced lectures will introduce many-body methods: static and dynamical mean-field theories, cluster methods, DMRG, tensor networks, and machine learning. Additional lectures will cover more explorative approaches, such as variational methods suitable for quantum computers and many-body solvers exploiting artificial neural networks. The lectures will show how the approaches can be used to unravel the mechanism of paradigmatic emergent phenomena in materials: non-conventional superconductivity, Mott phases, orbital ordering, topological phases of matter, the quantum Hall effect, and quantum spin-liquid phenomena. The topics will be treated with a focus on explaining key experiments in a realistic setting and an outlook on questions of materials design. Dedicated experimental lectures will explain the complexity of crystal-growth, cover experimental methods for characterizing many-body phases as well as experimental equilibrium and out-of-equilibrium probes of many-body states.