Open Problems in Strongly Correlated Electron Systems

In the last decade it has become increasingly evident that strong correla- tions between electrons are an essential and unifying factor in such diverse phenomena within solid state physics as high-temperature superconductivity, colossal magnetoresistance, the quantum Hall effect, heavy-fermion metals and Coulomb blockade in single-electron transistors. A new paradigmofnon- FermiLiquidbehaviourisalsoemergingand, inanumberofsystems, replacing the Fermi liquid, which has been the cornerstone ofthe physics of metals and superconductors for the pastdecades. In spite of major achievements, the theoretical studies and understanding of strongly-correlated electrons seems to be still in its infancy. Anomalous electron properties have been studied in some generic models of correlated electrons, such as the Hubbard and t-J models, the Anderson and Kondo impurity models, and their lattice equivalents. New insights into the behaviour of these, and related models is emerging from the introduction of powerful numerical methods to study such many-body models, including approximate techniquesofmany-body theory and exactresults inlow-andhigh-dimensional systems. Theseall showconvincingevidenceforbreakdownoftheFermiliquid concept. The Bled workshop focused on several major open questions in the theory of anomalous metals with correlated electrons. These theoretical advances were complemented by the latest experimental results in related materials, presented by leading experimentalists in the field. The main emphasis was on the following topics: - physics ofcuprates and high-temperature superconductors, - charge- and spin-ordering and fluctuations, - manganites and colossal magnetoresistance, - low-dimensional systems and transport, - Mott-Hubbard transition and infinite dimensional systems, - quantum Hall effect.