Field Theory in Condensed Matter Physics

• Fermi liquid theory: Fermi liquid ground state, quasiparticles and their stability, collective modes, Landau damping, non-Fermi liquids
• Luttinger liquids: pecularities of physics in one dimension, Luttinger model, basic of bosonization, correlation functions, relation to conformal field theories and two-dimensional classical XY model
• Superfluids and superconductors: physical properties of superfluids and superconductors, BCS theory, phase stiffness, vortices, rotating superfluids, boson-vortex duality in two dimensions, Berezinskii-Kosterlitz-Thouless transition, chiral superfluids and superconductors 
• Quantum Hall effect: basics of quantum Hall effect, flux attachment and Chern-Simons theory, topological order and anyons in fractional quantum Hall fluids, abelian Chern-Simons theory and the hierarchy of quanum Hall states, edge of quantum Hall fluids, non-abelian quantum Hall states, Dirac fermion duality

After successful completion of this module, the student is able to

• apply field theory techniques in condensed matter physics.
• understand theoretical paradigms that are central in modern condensed matter physics.
• understand the physics of Fermi liquids, one-dimensional Luttinger liquids, superfluids and superconductors, quantum Hall liquids. This knowledge provides a solid basis for entering the current research in quantum condensed matter physics.

No preconditions in addition to the requirements for the Master’s program in Physics.

In classroom lectures the content is presented on blackboard. Questions from students are welcome. The handwritten script will appear on the web-page of the lecture, where students can also find the relevant literature for self-study.

In tutorials we will discuss the solutions of home-work assignments which would provide students with a practical knowledge of the material discussed in the lecture and will prepare them for doing research in condensed matter physics.

Blackboard, complementary literature, discussions

1. T. Giamachi, Quantum Physics in One Dimension
2. E. Fradkin, Field Theories of Condensed Matter Physics
3. X.-G. Wen, Quantum Field Theory of Many-Body Systems
4. A. Altland & B. Simons, Condensed Matter Field Theory 
5. P. Coleman, Introduction to Many-Body Physics
6. S. Sachdev, Quantum Phase Transitions

There will be a written exam of 60 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample problems.

For example an assignment in the exam might be:

• Using perturbation theory, calculate the Landau parameters for fermions with a weak short-range potential.
• Analyze the fermionic energy spectrum and derive the Chern number of a chiral superconductor.
• Given the Chern-Simons effective theory, compute the charges and braiding phases of excitations.

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.