Role of localized electrons in electron-hole interaction: The case of SrTiO${}_3$

Strontium titanate ${\text{SrTiO}}_3$ is an extensively studied material. Of particular interest are its electronic properties. Here we present a theoretical study of its optical spectrum on the basis of state-of-the-art calculations including many-body effects. The latter are evaluated by solving the Bethe-Salpeter equation within the $GW$ approximation for the self-energy. Excitonic effects are strong at the onset and at higher energies up to 10 eV. Agreement between theory and experiment is excellent at the onset, but only qualitative at higher energies, where excitonic effects are stronger in theory than in experiment. The origin of structures in the spectrum, as well as the remaining discrepancy between theory and experiment, are discussed. We also present benchmark results for calculations using more approximate ways to determine the spectra, including simplified time-dependent density-functional theory.