Quantum Phase Transitions
Vorlesung im Vertiefungsgebiet "Theoretische Physik"
Lectures/Exercises
Mon, 13:00, BZW/A120
Thu, 11:10, BZW/A120
First lecture Apr 4, 2016
First exercise Apr 7, 2016
Exercise sheets
Problem sheet 1 (discussion Apr 7)
Problem sheet 2 (discussion Apr 21)
Problem sheet 3 (discussion May 9)
Problem sheet 4 (discussion Jun 2)
Problem sheet 5 (discussion Jun 16)
Problem sheet 6 (discussion Jun 30)
Problem sheet 7 (discussion Jul 14)
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. 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.
Contents
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
9. Quantum phase transitions in metals
10. Advanced topics: Quantum field theories, AdS/CFT, transport etc.
Literature
- S. Sachdev, Quantum Phase Transitions
- N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group
- I. Herbut, A Modern Approach to Critical Phenomena
- K. Yosida, Theory of Magnetism
- J. W. Negele & H. Orland, Quantum Many-Particle Systems
- A. Altlands & B. Simons, Condensed-Matter Field Theory