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→∞), 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.

PACS: 71.27.+a, 71.30.+h, 74.72.−h, 75.10.−b, 75.30.−m (all) DOI: 10.1070/PU2008v051n01ABEH006388 URL: https://ufn.ru/en/articles/2008/1/c/ 000256193500003 2-s2.0-44149107137 2008PhyU...51...23I Citation: Izyumov Yu A, Kurmaev E Z "Materials with strong electron correlations" Phys. Usp. 51 23–56 (2008) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks @article{Izyumov:2008, author = {Yu. A. Izyumov and E. Z. Kurmaev}, title = {Materials with strong electron correlations}, publisher = {Physics-Uspekhi}, year = {2008}, journal = {Phys. Usp.}, volume = {51}, number = {1}, pages = {23-56}, url = {https://ufn.ru/en/articles/2008/1/c/}, doi = {10.1070/PU2008v051n01ABEH006388} } Оригинал: Изюмов Ю А, Курмаев Э З «Материалы с сильными электронными корреляциями» УФН 178 25–60 (2008); DOI: 10.3367/UFNr.0178.200801b.0025