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
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
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. 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.
Dynamical Mean-Field Theory (DMFT) has opened new perspectives for the investigation of strongly correlated electron systems and greatly improved our understanding of correlation effects in models and materials. In contrast to Hartree-Fock-type approximations the mean field of DMFT is dynamical, whereby local quantum fluctuations are fully taken into account. DMFT becomes exact in the limit of high spatial dimensions or coordination number. Using DMFT the dynamics of correlated electron systems can be investigated non-perturbatively at all interaction strengths, electron densities and temperatures. By merging density functional theory with DMFT a powerful method for the calculation of the properties of correlated electron materials has become available, which is applicable to bulk systems and heterostructures, including topological states of matter. The inclusion of non-local correlations into DMFT makes it possible to explore unconventional superconductivity and the critical behavior at thermal or quantum phase transitions. By generalizing DMFT to non-equilibrium states also the real-time dynamics of correlated systems can be investigated. In this brief review the foundations and current status of DMFT are discussed along with characteristic physical insights obtained with this approach.
This volume contains the lectures delivered at the XIV Training Course in the Physics of Strongly Correlated Systems, held in Vietri sul Mare (Salerno) Italy, in October 2009. The project of the meeting was to promote the formation of young scientists by means of training through research. These features are reflected in the book: the lectures are up-to-date monographs of relevant subjects in the field of Condensed Matter Physics. Contributions include: Electronic Structure of Strongly Correlated Materials (Electronic structure calculations in one-electron approximation; Hubbard model in Dynamical Mean-Field Theory (DMFT); Electronic structure calculations for real materials by LDA+DMFT method); and, Computational Studies of Quantum Spin Systems (Quantum spin models, their ground states and quantum phase transitions; Classical phase transitions, Monte Carlo simulations, and finite-size scaling; Exact diagonalization methods; Quantum Monte Carlo simulations and the Stochastic Series Expansion method; and, Survey of related computational methods). Contributions also include: Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials (Mean-field theories for many-body systems; Lattice fermions in the limit of high dimensions; Dynamical mean-field theory for correlated lattice fermions; The Mott-Hubbard Metal-Insulator Transition; Electronic correlations and disorder; Theory of electronic correlations in materials; and, Kinks in the dispersion of strongly correlated electron systems).
The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean‐field picture as provided by Hartree‐Fock theory. Electronic correlations can have a very strong influence on the properties of materials. For example, they may turn a metal into an insulator (Mott‐Hubbard metal‐insulator transition). In these lecture notes I (i) introduce basic notions of the physics of correlated electronic systems, (ii) discuss the construction of mean‐field theories by taking the limit of high lattice dimensions, (iii) explain the simplifications of the many‐body perturbation theory in this limit which provide the basis for the formulation of a comprehensive mean‐field theory for correlated fermions, the dynamical mean‐field theory (DMFT), (v) derive the DMFT self‐consistency equations, and (vi) apply the DMFT to investigate electronic correlations in models and materials.