Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials

TL;DR

This paper introduces dynamical mean-field theory (DMFT), a powerful approach for understanding electronic correlations in materials, explaining its theoretical foundations, derivation, and applications to models and real materials.

Contribution

It provides a comprehensive overview of DMFT, including its derivation, self-consistency equations, and application to correlated electronic systems, advancing the theoretical framework.

Findings

DMFT captures metal-insulator transitions in correlated materials

Simplifies many-body problems in high lattice dimensions

Applied successfully to models and real materials

Abstract

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.