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

The cubic perovskite 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 non-local 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 non-local interactions and dynamical screening in determining the effective interaction strength of correlated compounds.