In compounds involving transition metal elements, Lanthanides or Anctinides the local Coulomb interaction between electrons in the partially filled d- or f-shells plays an important role. It is responsible for magnetism and other types of ordered ground states, and also strongly influences the properties of the paramagnetic phase. Well known phenomena here are the so-called heavy fermion behavior and the Mott-Hubbard metal insulator transition. The theoretical description of these materials poses a serious challenge. First, the complex lattice and electronic structure has to be reduced to a tractable model. Typically, two types of models emerge: When only one sort of electronic states dominates the Fermi energy, the Hubbard model is used, while for different electronic states mixing in the vicinity of the Fermi energy the periodic Anderson model is more appropriate. To study of low-energy dynamics and phase transitions, several tools have been devised over the past two decades. Here, two rather recent developments, the dynamical mean-field theory and the dynmacical cluster approximation, are used to calculate dynamics, including transport, of the paramagnetic and ordered phases at low or zero temperature. The equations resulting from the above theoretical schemes are solved with state-of-the-art computer algorithms, like quantum Monte-Carlo or numerical renormalization group schemes, using modern high-performance parallel computer systems.
Left: Phase diagram of the Hubbard model as function of doping and Coulomb energy. The vertical axis is scaled to compress the full inerval. Right: Metal-insulator transition and magnetic ordering at half filling for a Hubbard model with frustrated magnetic correlations.