2025-10-06 - 2025-10-10
Gautam Rai and Lorenzo Crippa
University of Hamburg
This set of lectures will provide a pedagogical introduction to the physics of correlated electronic materials. These are systems in which the Coulomb repulsion between electrons is so strong that the ground state wave function becomes many-body -- it cannot be approximated by the Slater determinant of single-particle wave functions. As a result, an exact description of the system is typically impossible, and one must find insightful ways to approximate the physics and simplify the problem.
The starting point of this course will be a brief review of solid-state concepts such as Bloch band theory and second quantization, followed by an introduction to the Green's function formalism for condensed matter physics. Next, we will derive the Fermi liquid description for weakly correlated materials, and discuss the collective modes thereof. We will describe the breakdown of the Fermi liquid paradigm with the introduction of Mott insulators. To discuss the Mott metal-insulator transition, we will introduce a powerful theoretical framework for the solution of correlated electron models, known as Dynamical Mean-Field Theory (DMFT).
In parallel to the theoretical lectures, we will introduce numerical methods for the modelling of simple electronic models, starting from band diagrams and ending with an application of DMFT to a paradigmatic model known as Bethe lattice.
