Correlated Electron Systems

The study of the correlated motion of electrons in solids is of increasing importance in condensed matter physics. In the past few years, the discovery of high-temperature superconductors has stimulated an enormous theoretical effort in this area, building on earlier theories of heavy-fermion and organic superconductors, and magnetic insulators. In a separate development, the discovery of the fractional quantum Hall effect stimulated research into the behaviour of the two-dimensional electron gas in a strong transverse magnetic field. The lectures give a systematic presentation of the current status of the theory in these areas. They cover the fractional quantum Hall effect and the many-body physics of the Hubbard model and its extension, paying particular attention to the properties of doped insulators which are relevant for high-temperature superconductivity. They detail discussions of situations for which controlled calculations may be carried out - specifically infinite dimensions, one dimension, and generalized models in which the fermions have N components and N to infinity.