Tilman Enss | Teaching — Condensed Matter Theory 2

as of March 2022

Condensed Matter Theory 2

Summer term 2022

This course introduces the concepts and methods of modern condensed matter theory. We will discuss metals, superconductors, magnetism and quantum liquids. We will introduce Green's functions and the diagrammatic technique, effective low-energy models, classical and quantum phase transitions. The exercises practise the different theoretical techniques and also show how to compute experimental observables.

Contents

1. Introduction
2. Green's functions and perturbation theory
   • Green's functions
   • Coherent states
   • Path integrals
   • Wick's theorem and perturbation theory
3. Metals
   • Jellium model
   • Charge excitations and screening
   • Phonons
4. Superconductivity
   • Fröhlich model
   • BCS theory of superconductivity
   • Hubbard model and high-Tc superconductors
5. Magnetism
   • Classical magnets (Ising, XY, Heisenberg) and phase transitions
   • Quantum magnets (transverse Ising) and quantum phase transitions
6. Quantum liquids
   • Landau Fermi liquid theory
   • Luttinger liquids

Lecture materials and homework problems (for participants)

Dates and Location

Lecture Monday and Wednesday 11.15-13.00h, Philosophenweg 12, kHS [LSF] starting April 20.
Tutorial Tuesday 9-11h, Philosophenweg 12, room 106, starting April 26.
Please register for access to lecture materials and to take the exam.

Prerequisites

• Condensed Matter Theory 1 (in particular second quantization and tight-binding lattice models as summarized in the CMT1 primer)
• Quantum Mechanics (PTP4)
• Theoretical Statistical Physics (MKTP1)

Literature

will be announced in the first lecture. Some recommended books:

• Ashcroft and Mermin, Solid State Physics
• Altland and Simons, Condensed Matter Field Theory
• Fetter and Walecka, Quantum Theory of Many-Particle Systems
• Negele and Orland, Quantum Many-Particle Systems
• Tinkham, Introduction to Superconductivity