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 $\text{Fe}3d$ 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 $\text{Fe}3d$ 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.

Figure 1

(Color online) Total DOS for LaOFeAs, $dpp$ Hamiltonian. Black line: LDA DOS. Red line: $\text{LDA}+\text{DMFT}$ DOS.

Figure 2

(Color online) Real (top) and imaginary (bottom) parts of the orbital-dependent self-energy in the $dpp$ Hamiltonian for $U=2.69$ and $J=0.79$.

Figure 3

(Color online) DOS of Fe orbitals in LaOFeAs, $dpp$ Hamiltonian. Color coding as in Fig. 1.

Figure 4

Momentum-resolved spectral function of LaOFeAs, $dpp$ Hamiltonian. Dark areas mark large spectral weight.

Figure 5

Comparison of the momentum-resolved spectral function of LaOFeAs at low energies. Upper panel: LDA. Lower panel: $\text{LDA}+\text{DMFT}$ $dpp$ Hamiltonian.

Figure 6

(Color online) Impurity spectral function within the $d$ Hamiltonian using interaction parameters $U=4.0\text{eV}$ and $J=0.7\text{eV}$ as have been used in Ref. 2. For those values a very correlated metal is obtained.

Figure 7

(Color online) DOS for ${\text{SrVO}}_3$, $d$-only model (small energy window). Top panel (a): Total DOS of LDA (black) and $\text{LDA}+\text{DMFT}$ (red). Bottom panel (b): LDA local orbitals (black), impurity spectral function $A\left(\omega \right)$ (red), and vanadium $t_{2g}$ partial DOS (green). Coulomb parameters for these calculations are given as inset.

Figure 8

(Color online) Total DOS for ${\text{SrVO}}_3$, $dp$ Hamiltonian (vanadium $t_{2g}$ and oxygen $p$).

Figure 9

(Color online) Quasiparticle renormalization $Z$ in a three-orbital Hubbard model. Calculations have been done using a semicircular DOS with bandwidth $W=4t$. Top panel: $n=3$ (half-filling). Bottom panel: $n=2$.