Green's functions for tight-binding systems

Quantum Condensed Matter Physics: Lecture 19 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 the Green's function formalism for non-interacting quantum many-body systems, such as generic tight-binding models (any fermionic model with a quadratic Hamiltonian). Starting from the basic building block of the retarded Green's function for a single quantum orbital, I build up the general theory and derive the general form of the Green's functions and spectral functions. I discuss the matrix representation, obtained from the resolvent of the Hamiltonian matrix, and recursive Green's function methods. As examples, I look at the Green's functions and density of states for the end and bulk of a 1d chain, as well as for simple models of molecules. Finally we look at a model describing a single molecule transistor, with a benzene molecule coupled to infinite leads. 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