Lecture notes of the Autumn School on Correlated Electrons 2018:Dieter Vollhardt: From Infinite Dimensions to Real Materials; Ole Andersen: From Materials to Models: Deriving Insight from Bands; Ferdi Aryasetiawan: Effective Electron-Electron Interaction in Many-Electron Systems; Marcus Kollar: The Foundations of Dynamical Mean-Field Theory; Michael Potthoff: Cluster Extensions of Dynamical Mean-Field Theory; Frank Lechermann: Charge Self-Consistency in Correlated Electronic Structure Calculations; Eva Pavarini: LDA+DMFT: Multi-Orbital Hubbard Models; Hao Tjeng: Determining Orbital Wavefunctions using Core-Level Non-Resonant Inelastic X-Ray Scattering; Hans Gerd Evertz: DMRG for Multiband Impurity Solvers; Fakher Assaad: Quantum Monte Carlo Methods for Fermion-Boson Problems; Erik Koch: Analytic Continuation of Quantum Monte Carlo Data; Hartmut Hafermann: Introduction to Diagrammatic Approaches; Thomas Maier: Dynamical Mean-Field and Dynamical Cluster Approximation Based Theory of Superconductivity; Karsten Held: Quantum Criticality and Superconductivity in Diagrammatic Extensions of DMFT; Martin Eckstein: Correlated Electrons out of Equilibrium: Non-Equilibrium DMFT
Lecture notes of the Autumn School on Correlated Electrons 2018:Dieter Vollhardt: From Infinite Dimensions to Real Materials; Ole Andersen: From Materials to Models: Deriving Insight from Bands; Ferdi Aryasetiawan: Effective Electron-Electron Interaction in Many-Electron Systems; Marcus Kollar: The Foundations of Dynamical Mean-Field Theory; Michael Potthoff: Cluster Extensions of Dynamical Mean-Field Theory; Frank Lechermann: Charge Self-Consistency in Correlated Electronic Structure Calculations; Eva Pavarini: LDA+DMFT: Multi-Orbital Hubbard Models; Hao Tjeng: Determining Orbital Wavefunctions using Core-Level Non-Resonant Inelastic X-Ray Scattering; Hans Gerd Evertz: DMRG for Multiband Impurity Solvers; Fakher Assaad: Quantum Monte Carlo Methods for Fermion-Boson Problems; Erik Koch: Analytic Continuation of Quantum Monte Carlo Data; Hartmut Hafermann: Introduction to Diagrammatic Approaches; Thomas Maier: Dynamical Mean-Field and Dynamical Cluster Approximation Based Theory of Superconductivity; Karsten Held: Quantum Criticality and Superconductivity in Diagrammatic Extensions of DMFT; Martin Eckstein: Correlated Electrons out of Equilibrium: Non-Equilibrium DMFT
1. Dieter Vollhardt: Understanding Correlated Materials with Lattice Fermions in Infinite Dimensions, 2. Robert Jones: Density Functional Theory for the Sceptical, 3. Eva Pavarini: Dynamical Mean-Field Theory for Materials, 4. Luca de' Medici: Hund's Metal Physics in the Iron-Based Superconductors, 5. Tim Wehling: DMFT for Moiré Systems, 6. Claude Ederer: Effect of Charge Self-Consistency in Calculations for Transition-Metal Oxides, 7. Jan Tomczak: A Perspective on Screened Coulomb Interactions from the constrained Random Phase Approximation, 8. Krzysztof Byczuk: Dynamical Mean-Field Theory for Correlated Electrons with Disorder, 9. Xavier Waintal: Learning Feynman Diagrams with Tensor Trains, 10. Philipp Werner: QMC for Nonequilibrium Systems, 11. Erik Koch: Analytic Continuation of Quantum Monte Carlo Data, 12. Walter Metzner: Functional Renormalization of Strongly Correlated Electrons: DMFT as a Booster Rocket, 13. Alexander Lichtenstein: Path Integrals and Reference Systems, 14. Karsten Held: Unconventional Superconductivity in the Dynamical Vertex Approximation, 15. Thomas Ayral: Dynamical Mean-Field Theory with Quantum Computing
1. Eva Pavarini: Dynamical Mean-Field Theory for Materials, 2. Xavier Gonze: Constrained Density-Functional Theory: Formalism, Algorithms and Applications, 3. Robert Eder: Green Functions and Self-Energy Functionals, 4. Erik Koch: Exact Diagonalization and Lanczos Method, 5. Ulrich Schollwöck: DMRG as Impurity Solver, 6. Riccardo Rossi: Diagrammatic Monte Carlo for the Hubbard Model, 7. Walter Metzner: Mean-Field Theory of Spin and Charge Order in the Two-Dimensional Hubbard Model, 8. Cécile Repellin: Introduction to Topological Phases in Condensed Matter, 9. Carsten Timm: Ginzburg-Landau Theory of Superconductivity, 10. Anna Böhmer: Experimental Characterization of Phase Transitions, 11. Markus Grüninger: From Mott to Cluster Mott: Probing Correlations with RIXS, 12. Matteo Mitrano: Light Control of Many-Body Phases, 13. Luca Tocchio: Variational Monte Carlo for the Hubbard Model, 14. Annabelle Bohrdt: Neural Quantum States for Strongly Correlated Systems, 15. Benedikt Fauseweh: Quantum Many-Body Simulations on Digital Quantum Computers
Since the first investigation of the Hubbard model in the limit of infinite dimensions by Metzner and Vollhardt, dynamical mean-field theory (DMFT) has become a very powerful tool for the investigation of lattice models of correlated electrons. In DMFT the lattice model is mapped on an effective quantum impurity model in a bath which has to be determined self-consistently. This approach led to significant progress in our understanding of typical correlation problems such as the Mott transition; furthermore, the combination of DMFT with ab-initio methods now allows for a realistic treatment of correlated materials. The focus of these lecture notes is on the relation between quantum impurity physics and the physics of lattice models within DMFT. Issues such as the observability of impurity quantum phase transitions in the corresponding lattice models are discussed in detail.
In this lecture we give an introduction to theoretical description of strongly correlated materials based on dynamical mean-¿eld theory (DMFT) and its extensions.The goal of this theoretical construction is to retain the many-body aspects of local atomic physics within the extended solid.The effects of short-range non-local correlations within cluster extensions of the DMFT scheme, as well as long-range Àuctuations within the fully renormalized dual-fermion perturbation scheme are discussed extensively.Recent progress in the numerical solution of the DMFT effective quantum impurity problem within the recently developed continuous-time Quantum Monte Carlo schemes is reviewed.We then describe realistic extensions of this approach which combine the accuracy of ¿rst-principle Density-Functional Theory with the treatment of local many-body effects within DMFT.
Abstract. The dynamical mean-field theory (DMFT) is a widely applicable approx-imation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particu-lar, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equa-tions, and present several applications which have provided important insights into the properties of correlated matter.
This text reviews, hopefully in a pedagogical manner, a series of work on the automatic calculations of Feynman diagrams in the context of quantum nanoelectronics (Keldysh formalism) with an application to the Kondo effect in the out-of-equilibrium single impurity Anderson model. It includes a discussion of (A) how to deal with the proliferation of diagrams, (B) how to calculate them using the Tensor Cross Interpolation algorithm instead of Monte-Carlo and (C) how to resum the obtained series. These notes correspond to a lecture given at the Autumn School on Correlated Electrons 2025 in Jullich, Germany. The book with all the lectures of the school (edited by Eva Pavarini, Erik Koch, Alexander Lichtenstein, and Dieter Vollhardt) is available in open access.