Condensed Matter Theory 2 (CMT2)

Course content

The aim of the course is to provide the student with an overview of modern topics in quantum condensed matter systems, including broken symmetry in quantum phases (superconductivity) and renormalization group, and to familiarize them with more advanced methods. The course uses both the operator version of many-body physics taught in Condensed Matter Theory 1, and the functional path integral methods, which will be introduced in the course. In addition, the course highlights some concept of topology applied to physical systems relevant for the research areas currently covered at NBI.

The microscopic origin of superconductivity is developed starting with the description of coupled electron-phonon systems and to make a link between the operator and path integral methods this is done in both ways. Then the renormalization group method is introduced and applied to various physical systems, for example ferromagnetic transitions, dissipative quantum tunneling, quantum impurity problems, and the Kosterlitz-Thouless transition.


M.Sc. Physics

Learning outcome

Participants are expected to learn to:

  • Explain the mechanism behind formation of a superconducting condensate
  • Use mean-field theory in fermionic many-body systems using both the operator and functional integral methods.
  • Apply the principle of renormalization group theory on quantum simple systems.
  • Read and explain to others modern theoretical literature in condensed matter physics

After the course, the student will understand the formulation of many-body physics in the language of coherent state path integrals and will be able to apply this to physical models for systems with broken symmetry, e.g. ferromagnetic transitions. The microscopic origin of superconductivity and the description of coupled electron-phonon systems will also be known. Furthermore, the student is familiar with the key elements of renormalization group applied to condensed matter systems, dissipative quantum tunneling, quantum impurity problems, and the Kosterlitz-Thouless transition.

This course will provide the students with a competent background for further studies within this research field, i.e. a M.Sc. project in theoretical condenses matter physics, and it will provide the students with mathematical tools that have application in range of fields within and beyond physics.

Lectures, exercises and project work.

1. "Condensed matter field theory", second edition, by A. Altland og B. Simons.
2.  Lecture notes.

Condensed Matter Theory 1 or similar and preferably Condensed Matter Physics 1&2 (Faststoffysik 1&2).

Restricted elective for specialisation "Quantum Physics"

7,5 ECTS
Type of assessment
Oral examination, 20 min
Continuous assessment
The evaluation has two components: (a) a 30 minute presentation of a research paper in front of the class (25%), and (2) a 20 minute oral exam without time for preparation (75%).
Without aids
Marking scale
7-point grading scale
Censorship form
No external censorship
More internal examiners
Criteria for exam assessment

Grade 12 is given for the independent and convincing achievement, documenting deep knowledge and insight on all aspects of the course goals. Grade 2 is given for the just acceptable achievement.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 28
  • Theory exercises
  • 28
  • Project work
  • 24
  • Exam
  • 1
  • Guidance
  • 4
  • Preparation
  • 121
  • English
  • 206