Materials with strong electron correlations

The electron structure and physical properties of strongly correlated systems containing elements with unfilled 3d, 4d, and 5f shells are analyzed. These systems include several transition metals, rare-earth elements, and actinides, as well as their numerous compounds, such as various oxides exhibiting metal–insulator phase transitions, cuprates, manganites, f systems with heavy fermions, and Kondo insulators. It is shown that the low-energy physics of such systems is described by three basic models: the Hubbard model, the sd-exchange model, and the periodic Anderson model under the condition that the on-site Coulomb repulsion energy $U$ or the sd exchange energy $J$ is of the order of the conduction-band width $W$. This situation does not involve a small parameter and should be treated nonperturbatively. We describe one such approach, the dynamic mean-field theory (DMFT), in which a system is considered to be only dynamically but not spatially correlated. We show that this approach, which is fully justified in the limit of large spatial dimensions ($d\to\infty$), covers the entire physics of strongly correlated systems and adequately describes the phenomena they exhibit. Extending the DMFT to include spatial correlations enables various d and f systems to be quantitatively described. Being a subject of intense development in recent years, the DMFT is the most effective and universal tool for studying various strongly correlated systems.