Textbook : "Green's Functions for Solid State Physicists" by S. Doniach and E.H. Sondheimer

I will follow the textbook closely. Chapters 1-5 introduce the Green's function formalism and give some basic applications. These will be covered in detail. A selection of topics from chapters 6-10 will be covered as the time permits.

Grades will be determined based on biweekly assignments and a student presentation (70/30). Presentations will be held towards the end of term. The scope, timing and the criteria for the presentations will be announced in class.

Course anouncements:

- The first
lecture will take place on
**Tuesday January 11**. As per UBC directive first four weeks classes are on-line. I will forward the zoom link to all registered students by email.

- Before the first lecture please read from the textbook:
- Introduction: The Theory of Condensed Matter (pages xvii-xix)
- Pages 1-5 from Chapter 1. I will start lecturing from Sec. 1.2.
- Please start thinking about you course presentation topic.
Consult this page for
presentation info and criteria.

**Effective Feb. 8 the lectures will be held in person in HENN-302.**- Office hours will be in a mixed mode: you are welcome to drop
by in person or use zoom links listed above.

**Schedule of student presentations**has been posted, see this page.

Assignments:

- Problem set #1 (due Jan. 26; please scan and email your solutions to the course TA rafaelhaenel(at)phas.ubc.ca) Solution
- Problem set #2 (due Feb. 10) Solution
- Problem set #3 (due March 3) Solution
- Problem set #4 (due March 17) Solution
- Problem set #5 (due April 7) Solution Solution

Please note: Working out the assignments is perhaps the single most important aspect of this course, absolutely essential for understanding the material. In order to receive credit assignment must be handed in by the end of the lecture on the due date. If you foresee a serious conflict that might prevent you from completing the problems by the due date please let me know ahead of time. I will consider extending the due date if there is a legitimate reason or if the conflict affects several students in the class. In fairness to other students who completed assignment on time, last minute requests for extension will not be granted.

You are welcome and encouraged to discuss problems with fellow students. However, when writing up answers

lec1

lec2

lec3

lec4

lec5

lec6

lec7

lec8

lec9

lec10

lec11

lec12

lec13

lec14

lec15

lec16

lec17

Course outline:

The course will present an introduction to Green's function methods in condensed matter physics. Green's functions are extremely useful in describing situations where exact solutions are not available and approximate methods for calculating physical observables are therefore required. This description covers most problems of interest in the contemporary condensed matter physics including systems with random disorder, electron-phonon interactions, electron-electron interaction, quantum spin systems, and cold atom systems. At the end of the course students will be able to perform basic calculations using Green's functions and will be able to follow more complex computations and arguments in the literature.

The course will introduce the Green's function formalism following closely chapters 1-5 in the textbook. Additional topics covered will depend to some degree on students' interests and may include:

- Dielectric response of a dense electron gas
- Random phase approximation

- The Hubbard model
- Magnetic properties of interacting electron systems
- X-ray singularity and Kondo problem
- Superconductivity

- Sachdev-Ye-Kitaev model