Recent Progress in First-Principles Methods for Computing the Electronic Structure of Correlated Materials

Abstract

Substantial progress has been achieved in the last couple of decades in computing the electronic structure of correlated materials from first principles. This progress has been driven by parallel development in theory and numerical algorithms. Theoretical development in combining ab initio approaches and many-body methods is particularly promising. A crucial role is also played by a systematic method for deriving a low-energy model, which bridges the gap between real and model systems. In this article, an overview is given tracing the development from the LDA+U to the latest progress in combining the GW method and (extended) dynamical mean-field theory (GW+EDMFT). The emphasis is on conceptual and theoretical aspects rather than technical ones.

Dynamical correlation enhanced orbital magnetization in VI$_{3}$

“…From the future perspective, effect of short-range or nonlocal correlations on the orbital magnetization would be interesting to study. It can be done using more accurate but computationally costly cluster methods [39,40], or GW+DMFT [41].…”

Ab Initio Full Cell GW+DMFT for Correlated Materials

“…Yet despite many successes, DFT+DMFT does not provide a truly parameter-free and quantitative ab initio theory of correlated materials, due to two closely related issues. First, the local Coulomb interaction in the DMFT impurity problem is typically treated as an adjustable Hubbard-like parameter [12], or is else estimated within another approximation [13]. Second, a double-counting correction [14,15] is required to remove the DFT contribution to the local interactions, but no consistently accurate double-counting correction is known [16].…”

Exploring the suitable theoretical approach for understanding the electronic and magnetic properties of $α$-Iron

“…The full many-body Hamiltonian equations of these systems are not exactly solvable using any present theoretical procedure. Thus in present days generally, there are two ways to get the approximate values of eigenfunctions and eigenvalues of these systems 9 . In first approach, generally few bands are considered for calculating some particular part of the full Hamiltonian, like Anderson impurity model 11 , Hubbard model 10 and so on.…”