Topology, Entanglement, and Strong Correlations
Abstract: Topology and entanglement are key concepts in many-body physics. Understanding the as-sociated emergent phenomena beyond toy models – in the world of real strongly-correlatedmaterials – requires the mastery of a wealth of different methods. These encompass analytical tools such as group theory, first principles techniques based on density-functional theory, materials-specific model-building schemes, as well as advanced modern numerical approaches for solving realistic many-body models. This year’s school provides an overview of the state-of-the art of these methods, their successes and their limitations. After introducing the basics, lectures will present the core concepts of topology and entanglement in many-body systems. To make contact to real materials, strategies for building materials specific models and techniques for their solution will be introduced. Among the latter, the school will cover quantum Monte Carlo methods, construction and optimization of correlated wave-functions, recursion and renormalization group techniques, as well as dynamical mean-field theory. More advanced lectures will give a pedagogical overview ontopological materials and their physics: topological metals, semimetals, and superconductors. Towards the end of the school entanglement in quantum dynamics and perspectives in quantum computation will be discussed. The goal of the school is to introduce advanced graduate students and up to these modern approaches for the realistic modeling of strongly correlated materials. A school of this size and scope requires backing from many sources. This is even more truethis year. As everywhere, the Corona pandemics provided scores of new challenges. Plans had to be changed and real facilities had to be replaced with virtual ones. We are very grateful forall the practical and financial support we have received. The Institute for Advanced Simulationat the Forschungszentrum Jülich and the Jülich Supercomputer Centre provided the major part of the funding and were vital for the organization and reorganization of the school as well as for the production of this book. The Institute for Complex Adaptive Matter (ICAM) supplied additional funds and ideas for successful online formats. The nature of a school makes it desirable to have the lecture notes available when the lecturesare given. This way students get the chance to work through the lectures thoroughly while their memory is still fresh. We are therefore extremely grateful to the lecturers that, despite tight deadlines, provided their manuscripts in time for the production of this book. We are confident that the lecture notes collected here will not only serve the participants of the school but will also be useful for other students entering the exciting field of strongly correlated materials.