Green's functions for interacting fermions

Quantum Condensed Matter Physics: Lecture 21

Theoretical physicist Dr Andrew Mitchell presents an advanced undergraduate / introductory Master's level lecture course on Quantum Condensed Matter Physics at University College Dublin. This is a complete and self-contained set of lectures, in which the theory is built up from scratch, and requires only a knowledge of basic quantum mechanics.

In this lecture I discuss Green's function techniques for interacting quantum systems. I show how the effect of electronic interactions, from the Coulomb interaction, can be incorporated into the Green's functions via the interaction "self-energy" using the Dyson equation, and provides an additional source of electronic scattering. We determine the Green's functions for such systems using both equations of motion methods and via the Lehmann representation. The former results in a complex set of coupled equations; we illustrate their use explicitly with the simple example of the Hubbard atom model. The latter requires the complete diagonalization of the Hamiltonian matrix in the many-particle basis, but is completely general. I illustrate this by application to the Anderson dimer model.

Navigate through the lectures of this course in order using the playlist:
https://www.youtube.com/playlist?list=PLotxEOxVaaoKRXdDN-7lI3Y88PaHqyOZL

Recommended course textbook: "Many-body quantum theory in condensed matter physics" by Bruss and Flensberg

Видео Green's functions for interacting fermions канала Dr Mitchell's physics channel