Theory of Condensed Matter

The course gives an introduction into the theory describing the emergence of macroscopic matter from interacting microscopic constituents.

This revolves around the explanation of emergence principles such as spontaneous symmetry breaking and long range order, adiabatic continuity, collective excitations such as Goldstone bosons, quasiparticles, and topological excitations, as they arise both in weakly- and strongly interacting systems.

We will explain the mathematical theories underlying the understanding of the following states of matter:

- The crystal, including the theory of quantum elasticity describing phonons and phonon interactions.

- Magnetism, with a focus on Mott-insulators and superexchange; spin-wave theory.

- Spin- and charge density waves in the weak coupling limit: the concept of nesting.

- The microscopic theory of superconductivity and superfluidity: from local pairs to the Bardeen-Cooper-Schrieffer theory.

- The Ginzburg-Landau effective field theory of macroscopic superconductivity.

- The Fermi-liquid including the origin of quasi-electrons, zero sound and plasmons.

With the help of the second quantization approach, perturbation theory and the mean-field theory the course introduces a number of fundamental concepts such as long-range order, spontaneous symmetry breaking, elementary, collective and topological excitations. These general concepts are illustrated on a range of archetypal examples such as crystalline solids, magnets, superfluids and superconductors and Fermi-liquid metals.