Simulating Correlations with Computers
Abstract: The combinatorial growth of the Hilbert space makes the many-electron problem one of the grand challenges of theoretical physics. Progress relies on the development of non-perturbative methods, based on either wavefunctions or self energies. This made, in recent years, calculations for strongly correlated materials a reality. These simulations draw their power from three sources: theoretical advances, algorithmic developments, and the raw power of massively parallel supercomputers. Turning to quantum hardware could give quantum materials science the ultimate boost. Before quantum parallelism can be exploited, however, many questions, algorithmic and engineering, need to be addressed. This year’s school will provide students with an overview of the state-of-the-art of manybody simulations and the promises of quantum computers. After introducing the basic modeling techniques and the concept of entanglement in correlated states, lectures will turn to methods that do not rely on wavefunctions, comparing density-functional theory, the GW method and dynamical mean-field approaches. Advanced lectures will broaden the discussion, addressing topics from the Luttinger-Ward functional to non-equilibrium Green functions. As a glimpse of future possibilities, the basics of quantum computing and its possible uses in materials simulations will be outlined.
A school of this size and scope requires backing from many sources. This is even more true during the Corona pandemics, which provided scores of new challenges. We are very grateful for all the practical and financial support we have received. The Institute for Advanced Simulation at the Forschungszentrum Jülich and the Jülich Supercomputer Centre provided the major part of the funding and were vital for the organization 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 lectures are 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.