DMFT at 25: Infinite Dimensions

Dynamical mean-field theory (DMFT) has opened new perspectives for dealing with strong electronic correlations and the associated emergent phenomena. This successful method has exploited the experience previously gained with single-impurity models, e.g., the Anderson model, transferring it to many-body lattice problems. The basis for this breakthrough was the realization, 25 years ago, that diagrammatic perturbation theory greatly simplifies in the limit of infinite dimensions, so that the self-energy becomes local. Nowadays DMFT, combined with $\textit{ab-initio}$ density-functional techniques, is the state-of-the art approach for strongly correlated materials. The lectures collected in this volume range from reconting the development of the dynamical mean-field theory to applications of the LDA + DMFT approach to real materials and modern developments. Among the latter, topics covered are modern impurity solvers, the calculation of two-particle Green functions, and method extensions beyond the single-site approximation. Lectures on photoemission spectroscopy provide the necessary contact to experiments. The goal of the school is to introduce advanced graduate students and up to the modern approaches to the realistic modeling of strongly-correlated systems. A school of this size and scope requires support and help from many sources. The DFG Research Unit FOR 1346 provided the framework for the school and a large part of the financial support. The Institute for Advanced Simulation and the German Research School for Simulation Sciences at the Forschungszentrum Jülich provided additional funding and were vital for the organization of the school and the production of this book. The Institute for Complex Adaptive Matter (ICAM) offered travel grants for selected international participants. 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. We are grateful to Mrs. H. Lexis of the Verlag des Forschungszentrum Jülich and to Mrs. D. Mans of the Graphische Betriebe for providing their expert support in producing the present volume on a tight schedule. We heartily thank our students and postdocs who helped in proofreading the manuscripts, often on quite short notice: Michael Baumgärtel, Khaldoon Ghanem, Esmaeel Sarvestani, Amin Kiani Sheikhabadi, Hermann Ulm, Guoren Zhang, and, in particular, our native speaker Hunter Sims. Finally, our special thanks go to Dipl.-Ing. R. Hölzle for his invaluable advice on the innumerable questions concerning the organization of such an endeavour, and to Mrs. L. Snyders and Mrs. E. George for expertly handling all practical issues