In the previous section we have already seen that in the case of strong electron–electron interactions, when the average interaction energy becomes larger than the corresponding kinetic energy, one can expect drastic changes of the properties of the system. Notably, the electrons will have a tendency to localize, so as to minimize their repulsion at the expense of a certain increase in kinetic energy. Materials and phenomena for which this factor plays an important role are now at the centre of activity of both experimentalists and theoreticians; this interest was especially stimulated by the discovery of high-Tc superconductivity in which electron correlations play a very important role. But even irrespective of the high-Tc problem, there are a lot of other interesting phenomena which are connected with strong electron–electron interactions. These phenomena include electron localization, orbital ordering and certain structural phase transitions, insulator–metal transitions, mixed valence and heavy fermion behaviour. The very existence of localized magnetic moments in solids, both in insulators and in metals, is actually determined by these correlations. That is why this is one of the most actively studied classes of phenomena at present.
Real materials to which one applies the models and the treatment presented in this chapter are mostly transition metal and rare earth compounds, although general ideas developed in this context are now applied to many other systems, including organic materials, nanoparticles or supercooled atoms. The typical situation in transition metal compounds is the one with partially filled d-shells.