Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2010-04-27
AIP Conference Proceedings vol. 1297 (American Institute of Physics, Melville, New York, 2010), p. 339
Physics
Condensed Matter
Strongly Correlated Electrons
Lecture Notes (65 pages, 26 figures), published version including corrections, published in "Lectures on the Physics of Strong
Scientific paper
10.1063/1.3518901
The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean-field picture as provided by Hartree-Fock theory. Electronic correlations can have a very strong influence on the properties of materials. For example, they may turn a metal into an insulator (Mott-Hubbard metal-insulator transition). In these lecture notes I (i) introduce basic notions of the physics of correlated electronic systems, (ii) discuss the construction of mean-field theories by taking the limit of high lattice dimensions, (iii) explain the simplifications of the many-body perturbation theory in this limit which provide the basis for the formulation of a comprehensive mean-field theory for correlated fermions, the dynamical mean-field theory (DMFT), (v) derive the DMFT self-consistency equations, and (vi) apply the DMFT to investigate electronic correlations in models and materials.
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