Condensed Matter II: Introduction to Green's function methods

PHYS 503, Spring 2022

Instructor:      Prof. Marcel Franz [Brim 461B, franz(at)physics(dot)ubc(dot)ca]
Lectures:         Tu&Th    14:00-15:30, HENN-302
Office hours:   Mo          14:00-15:00 and by appointment in Brim 461B (on zoom until Feb. 7, use this link)

Course TA:         Rafael Haenel [rafaelhaenel(at)phas.ubc.ca ]
TA office hours: Tue 16:00-17:00 in Brim 461 (on zoom until Feb. 7, use this link)

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 it is essential that you work alone. What you turn in must reflect your own understanding of each problem at the time of writing. Please do not copy solutions or let others copy your solution -- such a conduct violates academic integrity and can have serious consequences for your academic career.

Lecture Notes:

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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

Note of caution: Development of the Green's function methods normally involves considerable amount of mathematical formalism. While there is no way this can be avoided the Doniach-Sondheimer book has been chosen due to its minimalist approach: all developments are motivated from physical examples and the amount of formalism is kept at an absolute minimum necessary to find useful answers. Still, study of Green's functions requires patience and dedication. Hard work at the start will pay off eventually but the rewards first appear in chapter 5.