Dynamical mean-field theory within an augmented plane-wave framework: Assessing electronic correlations in the iron pnictide LaFeAsO

We present an approach that combines the local-density approximation (LDA) and the dynamical mean-field theory (DMFT) in the framework of the full-potential linear augmented plane-wave method. Wannier-type functions for the correlated shell are constructed by projecting local orbitals onto a set of Bloch eigenstates located within a certain energy window. The screened Coulomb interaction and Hund's coupling are calculated from a first-principles constrained random-phase approximation scheme. We apply this $\text{LDA}+\text{DMFT}$ implementation, in conjunction with a continuous-time quantum Monte Carlo algorithm, to the study of electronic correlations in LaFeAsO. Our findings support the physical picture of a metal with intermediate correlations. The average value of the mass renormalization of the $\text{Fe}\text{ }3d$ bands is about 1.6, in reasonable agreement with the picture inferred from photoemission experiments. The discrepancies between different $\text{LDA}+\text{DMFT}$ calculations (all technically correct) which have been reported in the literature are shown to have two causes: (i) the specific value of the interaction parameters used in these calculations and (ii) the degree of localization of the Wannier orbitals chosen to represent the $\text{Fe}\text{ }3d$ states, to which many-body terms are applied. The latter is a fundamental issue in the application of many-body calculations, such as DMFT, in a realistic setting. We provide strong evidence that the DMFT approximation is more accurate and more straightforward to implement when well-localized orbitals are constructed from a large energy window encompassing $\text{Fe-}3d$, $\text{As-}4p$, and $\text{O-}2p$ and point out several difficulties associated with the use of extended Wannier functions associated with the low-energy iron bands. Some of these issues have important physical consequences regarding, in particular, the sensitivity to the Hund's coupling.