Electronic structure calculations using dynamical mean field theory

TLDR

Electronic structure calculations are challenging for strongly correlated materials, and the standard LDA approach fails to capture these correlations. The paper reviews the LDA + DMFT method and explores alternative implementations, such as replacing the LDA part with GW. LDA + DMFT combines density‑functional theory with dynamical mean‑field theory, solving the DMFT equations using impurity solvers tailored for multi‑orbital systems to capture weakly or strongly correlated phases. The method is considered a breakthrough and has been successfully applied to a wide range of materials, including Pu, Ce, Fe, Ni, and many transition‑metal oxides.

Abstract

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.