1. knows and understands the description of condensed-matter systems using effective microscopic models and field theories based on the formalism of 2nd quantisation.
2. understands the range of applicability of effective models and the main problems arising in the description of real systems like solids or ultracold atoms.
3. can calculate observables such as the energy spectrum, correlation functions or electric currents using field-theoretical methods like linear response theory.
4. knows and understands advanced concepts appearing in condensed-matter physics such as quantum phase transitions, topological excitations or collective phenomena.
5. knows and understands advanced field-theoretical methods such as renormalisation-group methods, non-equilibrium quantum field theory or bosonisation and can use them to describe condensed-matter systems.
The aim of this course is the application of methods of statistical field theory to condensed-matter systems. This includes the description of these systems using field-theoretical methods, the discussion of their range of applicability, and the calculation of experimental observables. Possible condensed-matter systems to be discussed in the course include magnetism of antiferromagnets and magnetically frustrated systems, disordered systems, quantum Hall effect, topological insulators, superconductivity, one-dimensional electronic and magnetic systems, quantum dots and nanostructures, as well as ultracold atomic and ionic gases. The course also covers necessary advanced methods to treat these systems, for example path integrals for spin systems, renormalisation-group methods, non-equilibrium quantum field theory, quantum field theory for open systems, bosonisation, or non-linear sigma models.