Quantum Phase Transitions

Vorlesung im Wahlpflichtvertiefungsgebiet "Theoretische Physik" (VWm)

Lectures/Exercises

Monday (2), 9:20h-10:50h, BZW/A120/P
Friday (4), 13:00h-14:30h, BZW/A120/P

First lecture: Apr 9, 2018
First exercise: Apr 20, 2018
Course language: English
Instructor: Dr. Lukas Janssen

Problem Sheets

Problem Sheet 1 (discussion Apr 20)
Problem Sheet 2 (discussion May 4)
Problem Sheet 3 (discussion May 18 and June 8)
Problem Sheet 4 (discussion June 8)
Problem Sheet 5 (discussion June 25)
Problem Sheet 6 (discussion July 6)
Problem Sheet 7 (discussion July 20)

Handwritten Lecture Notes

(will be posted after the chapter has been discussed in class)
1. Introduction
2. Classical phase transitions and universality
3. Statistical mechanics and path integrals
4. Renormalization group
5. Theoretical models for quantum phase transitions
6. Quantum phase transitions: Primer
7. Magnetic quantum phase transitions
8. Quantum phase transitions of bosons and fermions

Description

Quantum Phase Transitions have become an important research area of modern condensed matter physics. Such transitions occur at zero temperature upon varying a non-thermal 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 multiplicity 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 Master students and PhD students, as well as for Bachelor students who are 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. Scherer, Introduction to Renormalization (lecture notes, University of Cologne, 2017)
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

Lukas Janssen