When strong correlations become weak: Consistent merging of $GW$ and DMFT

The cubic perovskite ${\mathrm{SrVO}}_3$ is generally considered to be a prototype strongly correlated metal with a characteristic three-peak structure of the $d$-electron spectral function, featuring a renormalized quasiparticle band in between pronounced Hubbard sidebands. Here we show that this interpretation, which has been supported by numerous “ab initio” simulations, has to be reconsidered. Using a fully self-consistent $GW$ + extended dynamical mean-field theory calculation we find that the screening from nonlocal Coulomb interactions substantially reduces the effective local Coulomb repulsion, and at the same time leads to strong plasmonic effects. The resulting effective local interactions are too weak to produce pronounced Hubbard bands in the local spectral function, while prominent plasmon satellites appear at energies which agree with those of the experimentally observed sidebands. Our results demonstrate the important role of nonlocal interactions and dynamical screening in determining the effective interaction strength of correlated compounds.

Figure 1

Different levels of approximation in the multi-tier $GW$ + EDMFT scheme: The LDA + $G^0{W}^0$ treatment of the full range of bands (tier III) is used to construct the effective model for the intermediate energy space of Wannier functions (tier II), which is handled in $GW$. An effective model for the local part (potentially further reduced in number of orbitals) of tier II is constructed and handled as the EDMFT impurity problem (tier I). Tiers I and II are solved self-consistently.

Figure 2

Local spectral function of ${\mathrm{SrVO}}_3$ calculated in different approximations: Single shot $G^0{W}^0$, self-consistent $GW$, and $GW$ + EDMFT.

Figure 3

Fully screened interaction for ${\mathrm{SrVO}}_3$ in one-shot $G^0{W}^0$, self-consistent $GW$, and $GW$ + EDMFT.

Figure 4

$\mathbf{k}$-resolved spectral function from DMFT with screened local $U\left(\omega \right)$ taken from cRPA, $GW$ + EDMFT, and one-shot $G^0{W}^0$. For easier comparison, lines mark the maxima of the spectra.