Electronic structure calculations using dynamical mean field theory

• Published in: Advances in physics Vol. 56; no. 6; pp. 829 - 926
• Main Author: Held, K.
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis Group 01.11.2007; Taylor & Francis
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electron states; Exact sciences and technology; Magnetic properties and materials; Magnetotransport phenomena, materials for magnetotransport; Manganites; Methods of electronic structure calculations; Physics; Band structure; Mean field approximation; Oxides; Giant magnetoresistance; Random phase approximation; Electronic structure; Rare earths; Transition elements; Scaling laws; Density functional method; Strongly correlated electron systems; Ferromagnetism; Dynamic model; Green's function methods; Manganites; Local density approximation
• ISSN: 0001-8732; 1460-6976
• DOI: 10.1080/00018730701619647

The calculation of the electronic properties of materials is an important task of solid-state theory, albeit particularly difficult if electronic correlations are strong, e.g., in transition metals, their oxides and in f-electron systems. The standard approach to material calculations, the density functional theory in its local density approximation (LDA), incorporates electronic correlations only very rudimentarily and fails if the correlations are strong. Encouraged by the success of dynamical mean field theory (DMFT) in dealing with strongly correlated model Hamiltonians, physicists from the bandstructure and the many-body communities have joined forces and developed a combined LDA + DMFT method recently. Depending on the strength of electronic correlations, this new approach yields a weakly correlated metal as in the LDA, a strongly correlated metal or a Mott insulator. This approach is widely regarded as a breakthrough for electronic structure calculations of strongly correlated materials. We review this LDA + DMFT method and also discuss alternative approaches to employ DMFT in electronic structure calculations, e.g., by replacing the LDA part with the so-called GW approximation. Different methods to solve the DMFT equations are introduced with a focus on those that are suitable for realistic calculations with many orbitals. An overview of the successful application of LDA + DMFT to a wide variety of materials, ranging from Pu and Ce, to Fe and Ni, to numerous transition metal oxides, is given.