Quantum Phase Transitions (Summer 26)
Master level course in specialization area "Theoretical Physics" (VWm)
Course language: English
Instructor: Dr. Lukas Janssen
Table of contents
Coordinates
Monday (2), 9:20h-10:50h, BZW/A120/P
Friday (2), 9:20h-10:50h, BZW/A120/P
Content & Lecture Notes
(handwritten notes will be posted after chapter has been discussed in class)
- Introduction
- Classical phase transitions and universality
- Statistical mechanics and path integrals
- Renormalization group
- Theoretical models for quantum phase transitions
- General aspects of quantum phase transitions
- Magnetic quantum phase transitions
- Quantum phase transitions of bosons and fermions
Homework
(problem sets will be posted at least a week before their discussion in class)
Problem Set #1 (discussion April 24)
Problem Set #2 (discussion May 11)
Problem Set #3 (discussion June 1)
Problem Set #4 (discussion June 12)
Problem Set #5 (discussion June 26)
Problem Set #6 (discussion July 6)
Problem Set #7 (discussion July 17)
Video Recordings
Recordings from Summer 2024 are available on videocampus.sachsen.de.
Schedule
| Week | Monday | Friday | ||
|---|---|---|---|---|
| 16 | 13.04.26 | Lecture | 17.04.26 | Lecture |
| 17 | 20.04.26 | Lecture | 24.04.26 | Exercise #1 |
| 18 | 27.04.26 | Lecture | 01.05.26 | Bank holiday |
| 19 | 04.05.26 | Lecture | 08.05.26 | Lecture |
| 20 | 11.05.26 | Exercise #2 | 15.05.26 | Lecture |
| 21 | 18.05.26 | Lecture | 22.05.26 | Lecture |
| 22 | 25.05.26 | Bank holiday | 29.05.26 | Lecture (watch the video if you cannot attend in person) |
| 23 | 01.06.26 | Exercise #3 | 05.06.26 | Lecture |
| 24 | 08.06.26 | Lecture | 12.06.26 | Exercise #4 |
| 25 | 15.06.26 | Lecture | 19.06.26, 07:30 19.06.26, 09:20 |
Lecture Lecture |
| 26 | 22.06.26 | No class (shifted to 29.05.26) |
26.06.26, 07:30 26.06.26, 09:20 |
Lecture Exercise #5 |
| 27 | 29.06.26 | Lecture |
03.07.26, 07:30 |
Lecture Lecture |
| 28 | 06.07.26 | Exercise #6 | 10.07.26 | Lecture |
| 29 | 13.07.26 | No class (shifted to 19.06.26) |
17.07.26 | Exercise #7 |
| 30 | 20.07.26 | No class (shifted to 26.06.26) |
24.07.26 | No class (shifted to 03.07.26) |
Registration
- B.Sc. & M.Sc. students: Online through selma
- Ph.D. students: In class on 13.04.26 or 17.04.26
Description
Quantum phase transitions have become an important research area of modern condensed matter physics. These transitions occur at absolute zero temperature upon varying a nonthermal control parameter such as pressure, magnetic field, or chemical composition. The presence of a continuous quantum phase transition can influence the observable finite-temperature properties of a system over a wide range of parameters, with a variety of new and unexpected phenomena, including the possible emergence of non-Fermi liquid behavior and high-temperature superconductivity.
The lecture will give an introduction to the field from the perspective of condensed-matter physics. It will cover concrete model systems for quantum phase transitions, universal aspects of classical and quantum critical phenomena, theoretical methods such as quantum field theories and the renormalization group, as well as advanced topics including related aspects in high-energy physics. Relevant experimental observations will be discussed as well.
The lecture is suitable for M.Sc. and Ph.D. students, as well as for B.Sc. students familiar with second quantization. Basic knowledge in many-particle theory (Green's functions, mean-field theory, diagrammatics) is helpful.
Literature
- I. Herbut, A Modern Approach to Critical Phenomena (Cambridge University Press, 2007)
- S. Sachdev, Quantum Phase Transitions (Cambridge University Press, 2011)
- M. Vojta, Thermal and Quantum Phase Transitions (lecture notes, Les Houches Doctoral Training School in Statistical Physics, 2015)
- J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford University Press, 2002)
Contact
Dr. L. Janssen
Emmy Noether Group "Quantum Critical Matter"