(a) Cuprate superconductor levitates a magnet, (b) Band structure and density of states of a material probed by ARPES (c) ARPES (Angle resolved photoemission spectroscopy) technique (d) Richard P. Feynman

Many body physics provides the framework for understanding the collective behavior of interacting electrons in a material. This course provides an introduction to the field, familiarize you with the main techniques and concepts, aiming to give you first-hand experience in calculations and problem solving using many body methods.

Class Time: ARC building (204), 12:10pm-1:30pm every Monday and Thursday

Literature: The course will be built from the three excellent books:

1. Condensed Matter Field Theory by Alexander Atland and Ben Simons
Most of the course is build from this bool. It is a modern textbook on Field Theory with strong emphasis on modern tools like Functional field integral.
2. Quantum Many-particle Systems by J.W. Negele, H. Orland
Excellent coverage of perturbation theory using Functional field integral language. We will use it in the chapter on perturbation theory.
3. Many-Particle Physics by Gerald D. Mahan
A classical textbook dealing in detail with response functions such as Green's function and optical conductivity, Kubo formalism and many more. We will add a small bits and pieces from this book, mostly in the chapter on the perturbation theory & uniform electron gas.

1. Introduction to Many Body Physics by Piers Coleman
Very exhaustive reference with particular emphasis on correlations.
2. Methods of Quantum Field Theory in Statistical Physics by A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinski
Classic text from the sixties, known usually as AGD. Technically a bit more involved but contains many derivations which can not be found in any other book.
3. Basic Notion of Condensed Matter Physics by P.W. Anderson
Great inspiration from one of the "fathers" of strongly correlated field
4. Quantum Theory of Many-Particle Systems by A.L. Fetter and J.D. Walecka
5. Field Theories of Condensed Matter Systems by Edwardo Fradkin
Interesting material on the fractional statistics and the fractional quantum Hall effect.
6. Introduction ot Superconductivity by Michael Tinkham
Great book on supeconductivity.
7. Interacting Electrons and Quantum Magnetism by Assa Auerbach
8. Quantum Field Theory in Condensed Matter Physics by Alexei M. Tsvelik
Very good for one dimensional systems.

Lecture Notes from 2022 in pdf

Homeworks from 2022

1. Quantum fields
2. Second quantization
3. Applications of second quantization:
1. Jellium model
2. Tight binding model
3. Mott Hubbard transition and Spin models of Mott insulator
4. Interacting fermions in 1D
5. Quantum spin chain
4. Feynman path integral
5. Functional field integral
6. Green's function at zero temperature and finite temperature (Matsubara formalism)
7. Perturbation Theory
8. Plasma theory of interacting electron gass
9. Bose-Einstein condensation and superfluidity
10. Superconductivity & BCS Theory

Students with Disabilities