Quantum Phase Transitions (Summer 24)

Master level course in specialization area "Theoretical Physics" (VWm)
Course language: English
Instructors: Dr. Lukas Janssen (lectures) and Dr. Zihong Liu (exercises)

Coordinates

Monday (2), 9:20h-10:50h, BZW/A120/P
Friday (2), 9:20h-10:50h, WIL/C129/H (ATTENTION: new room!) (exception on 31.05.24: SE2/201/H)

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

TeX-typed lecture notes (courtesy of Tim Pokart)

Homework 

(problem sets will be posted at least a week before their discussion in class)

Problem Set #1 (discussion April 19)
Problem Set #2 (discussion May 3)
Problem Set #3 (discussion May 27)
Problem Set #4 (discussion June 7)
Problem Set #5 (discussion June 21)
Problem Set #6 (discussion July 12)
Problem Set #7 (discussion July 22)

Video Recordings

(lecture recordings will be posted on videocampus.sachsen.de and linked here)

Lecture 01 (08.04.24): Introduction
Lecture 02 (12.04.24): Classical phase transitions and universality I
Lecture 03 (15.04.24): Classical phase transitions and universality II
Lecture 04 (22.04.24): Classical phase transitions and universality III
Lecture 05 (26.04.24): Classical phase transitions and universality IV
Lecture 06 (29.04.24): Statistical mechanics and path integrals I
Lecture 07 (06.05.24): Statistical mechanics and path integrals II
Lecture 08 (10.05.24): Renormalization group I
Lecture 09 (13.05.24): Renormalization group II
Lecture 10 (17.05.24): Renormalization group III
Lecture 11 (31.05.24): Renormalization group IV
Lecture 12 (03.06.24): Renormalization group V & Theoretical models for quantum phase transitions I
Lecture 13 (10.06.24): Theoretical models for quantum phase transitions II & General aspects of quantum phase transitions I
Lecture 14 (14.06.24): General aspects of quantum phase transitions II
Lecture 15 (17.06.24): General aspects of quantum phase transitions III
Lecture 16 (24.06.24): General aspects of quantum phase transitions IV
Lecture 17 (28.06.24): Magnetic quantum phase transitions I
Lecture 18 (01.07.24): Magnetic quantum phase transitions II
Lecture 19 (05.07.24): Magnetic quantum phase transitions III & Quantum phase transitions of bosons and fermions I
Lecture 20 (08.07.24): Quantum phase transitions of bosons and fermions II
Lecture 21 (08.07.24): Quantum phase transitions of bosons and fermions III

Schedule

Registration

• B.Sc. & M.Sc. students: Online through selma
• Ph.D. students: In class on 08.04.24 or 12.04.24

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"