Condensed Matter Theory 1 (CMT1)

Course content

This course is an introduction to quantum field theoretical methods aimed for both experimentalists and theorists with particular focus on condensed matter physics. The content spans a wide range of topics necessary for understanding concepts and methods used in advanced solid state physics. Finally, the course provides a good foundation for the course CMT2 and for doing active research in condensed matter physics at the Niels Bohr Institute.

In the course, we  focus on the interacting electron gas, describing metals and semiconductors, and use this as an example to illustrate the techniques taught. The course is meant to teach the fundamental filed-theoretical concepts and techniques such as second quantization, equations of motion for operators, many-particle Green functions at finite temperatures, and Feynman diagrams.

Education

M.Sc. Physics

Learning outcome

Skills

Participants are expected to learn to:

  1. Describe an interaction quantum mechanical many-particle system by the use of second quantization.
  2. Handle (for example (anti)commuting mixed products of) boson and fermion quantum field operators in various representations (Schrodinger, Heisenberg, and the interaction picture).
  3. Use real-time and Matsubara Green functions to solve interacting many-body problems.
  4. Use mean-field theory to simplify interacting Hamiltonians to simpler manageable problems.
  5. Use equation of motions techniques to obtain Greens functions.
  6. Derive and use Feynman rules for perturbation theory within potential scattering, electron-electron, and electron-phonon interactions.
  7. Perform a detailed calculation and regularization of the ground state energy for the interacting electron gas including the screening of long-range Coulomb interactions and its Landau damped plasmons.
  8. Describe single-particle excitations in an interacting many-particle system in terms of renormalized quasi-particles. This includes being able to obtain effective masse and charge, Fermi surfaces, Z-factors and lifetimes.
  9. To use all these acquired skills to solve relevant physics problems, including mainly issues within the physics of solid materials, nano-scopic systems, quantum liquids and ultracold atomic gasses.

Knowledge
In the course, we focus on the interacting electron gas, describing metals and semiconductors, and use this as an example to illustrate the techniques taught. The course is meant to teach the fundamental filed-theoretical concepts and techniques such as second quantization, equations of motion for operators, many-particle Green functions at finite temperatures, and Feynman diagrams.

Competences
This course will provide the students with the required background for further studies within this research field, i.e. the course CMT2 or a master thesis. The course will provide most of the modern formalism used in the scientific literature on condensed matter physics.

Lectures and exercises

Henrik Bruus and Karsten Flensberg: Many-Body Quantum Theory in condensed Matter Physics", Oxford University Press

Basic knowledge of theory of functions of complex variables is expected.

Restricted elective for specialisation "Quantum Physics"

ECTS
7,5 ECTS
Type of assessment
Written assignment, 24 timer
24-hour take-home assignment
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
  • Practical exercises
  • 28
  • Exam
  • 24
  • Preparation
  • 126
  • English
  • 206