Quantum systems for which interactions among the ``elementary''
constituents, say electrons, are effectively strong
is nowadays referred to as strongly correlated systems.
The most prominent examples of strongly correlated electronic systems
are systems displaying the fractional quantum Hall effect and high-temperature
superconductivity. The simple metallic model by which electrons
are treated as an essentially non-interacting gas (the Fermi-Liquid theory)
is invalidated by the correlations induced through the effectively
strong Coulomb interaction in strongly correlated electronic systems.
There are many more examples of strongly correlated systems
among organic materials and heavy fermions compounds.
From a conceptual point of view, the trademark of strongly correlated
systems is that perturbation theory around the idealization of
the Fermi gas breaks down. Aside for one-dimensional physics,
there are essentially no known reliable non-perturbative technique
available to us to this date to confront strongly correlated systems.
This is certainly true of analytical approaches.
Moreover, numerical approaches suffer greatly from the relatively
small system sizes that are currently accessible.
The study of strongly correlated systems thus represents one of the
new frontiers of condensed matter physics.
Dr. Christopher Mudry
Paul Scherrer Institut
WHGA/125
CH-5232 Villigen PSI
Switzerland