Electron interactions and the Hubbard model

Quantum Condensed Matter Physics: Lecture 16

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 strongly correlated electron physics and the Hubbard model. I explain why electronic interactions beyond a simple tight-binding description is such a challenge for theoretical physics, and discuss some of the approximations used to understand the rich range of physics contained within the Hubbard model. I discuss the Mott metal-insulator transition, itinerant ferromagnetism, antiferromagnetism in certain insulating phases, and also derive from first principles a perturbative approach which we use to obtain the Heisenberg spin model from the Hubbard model in the strong-interaction limit.

Navigate through the lectures of this course in order using the playlist:
   • Quantum condensed matter physics lecture p...  

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