Correlated fermions: a new paradigm in physics on the example of solid-state physics?

We review briefly the properties and provide an elementary theoretical description of correlated fermion systems, based mainly on the example of electronic systems undergoing metal-insulator (Mott-Hubbard) transition, which represents a transformation of electron gas (delocalized states) into atomic configuration with localized spins. The crystallization of liquid 3He and the delocalization of nuclei into an extended system (neutron star) are also mentioned as two other examples. The characterization of the Mott-Hubbard transition as a quantum phase transformation is stressed. In such systems the localized (atomic) and delocalized (plane-wave-like) states can coexist when the transition is of a discontinuous nature, i.e. at non-zero temperature. We also discuss briefly other condensed fermionic systems such as heavy fermions, high-temperature superconductor systems, systems with a colossal magnetoresistance, and correlated quantum dots, in order to further illustrate the uniqueness of these systems among various Fermi liquids or magnetic semiconductors. (author)