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JOURNALS // Uspekhi Fizicheskikh Nauk // Archive

UFN, 2008 Volume 178, Number 1, Pages 25–60 (Mi ufn552)

This article is cited in 51 papers

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Materials with strong electron correlations

Yu. A. Izyumov, È. Z. Kurmaev

Institute of Metal Physics, Ural Division of the Russian Academy of Sciences

Abstract: 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.

PACS: 71.27.+a, 71.30.+h, 74.72.-h, 75.10.-b, 75.30.-m

Received: April 10, 2007
Revised: September 6, 2007

DOI: 10.3367/UFNr.0178.200801b.0025


 English version:
Physics–Uspekhi, 2008, 51:1, 23–56

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