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We investigate the electronic structure of SrMnO$_3$ with Density FunctionalTheory (DFT) plus Dynamical Mean-Field Theory (DMFT). Within this scheme theselection of the correlated subspace and the construction of the correspondingWannier functions is a crucial step. Due to the crystal field splitting of theMn-$3d$ orbitals and their separation from the O-2$p$ bands, SrMnO$_3$ is amaterial where on first sight a 3-band $d$-only model should be sufficient.However, in the present work we demonstrate that the resulting spectrum isconsiderably influenced by the number of correlated orbitals and the number ofbands included in the Wannier function construction. For example, in a $d$-$dp$model we observe a splitting of the \tg lower Hubbard band into a more complexspectral structure, not observable in $d$-only models. To illustrate thesehigh-frequency differences we employ the recently developed Fork Tensor ProductState (FTPS) impurity solver, as it provides the necessary spectral resolutionon the real-frequency axis. We find that the spectral structure of a 5-band$d$-$dp$ model is in good agreement with PES and XAS experiments. Our resultsdemonstrate that the FTPS solver is capable of performing full 5-band DMFTcalculations directly on the real-frequency axis.

Dynamical Mean-Field Theory on the Real-Frequency Axis: p-d Hybridizations and Atomic Physics in SrMnO$_3$