Condensed Matter Theory 2

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
   1. Green's functions
   2. Coherent states
   3. Path integrals
   4. Wick's theorem and perturbation theory
3. Metals
   1. Hartree-Fock
   2. Jellium model
   3. Charge excitations and screening
   4. Phonons
4. Superconductivity
   1. Electron-phonon coupling (Fröhlich model)
   2. Cooper bound state
   3. BCS theory of superconductivity
   4. Pair propagator
   5. Effective action
      
   6. Hubbard model and high-Tc superconductors
5. Magnetism
   1. Classical magnets (Ising, XY, Heisenberg) and phase transitions
   2. Stoner ferromagnetism
   3. Transverse field Ising model
   4. Classical and quantum phase transitions
6. Quantum liquids
   1. Landau Fermi liquid theory
   2. Luttinger liquids

Dates and Location

Lecture Monday and Wednesday 11.15-13.00h, Philosophenweg 12, kHS.
Tutorial Tuesday 9.15-11.00h, Phil 12 room 106.
The written exam takes place on Monday 1st August, 11-13h.
 

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
• Di Castro and Raimondi, Statistical Mechanics and Applications in Condensed Matter, Cambridge 2015
• Fetter and Walecka, Quantum Theory of Many-Particle Systems
• Negele and Orland, Quantum Many-Particle Systems
• Sachdev, Quantum Phase Transitions, Cambridge 2011
• Tinkham, Introduction to Superconductivity