Autumn School on Correlated Electrons. Correlated Materials: Methods and Applications

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.

Topics: strongly correlated systems, Hubbard model, phase transitions; neural quantum states, many-body methods, QMC, DMFT and DFT+DMFT, Quantum Many-body Simulations on Digital Quantum Computer, RIXS experiments, Lanczos Method, Light-Control of Many-Body Phases, Quantum Spin Liquids, Topological Phases, DMRG, Ginzburg-Landau Theory of Superconductivity, Variational Monte Carlo.