The recent discovery of superconductivity in hole-doped NdNiO$_2$ thin films has captivated the condensed matter physics community. Such compounds with a formal Ni$^+$ valence have been theoretically proposed as possible analogues of the cuprates, and the exploration of their electronic structure and pairing mechanism may provide important insights into the phenomenon of unconventional superconductivity. At the modeling level, there are however fundamental issues that need to be resolved. While it is generally agreed that the low-energy properties of cuprates can to a large extent be captured by a single-band model, there has been a controversy in the recent literature about the importance of a multi-band description of the nickelates. The origin of this controversy is that studies based entirely on density functional theory (DFT) calculations miss important correlation and multi-orbital effects induced by Hund coupling, while model calculations or simulations based on the combination of DFT and (extended) dynamical mean field theory ((E)DMFT) involve ad-hoc parameters and double counting corrections that substantially affect the results. Here we use a multi-site extension of the recently developed $GW$+EDMFT method, which is free of adjustable parameters, to self-consistently compute the interaction parameters and electronic structure of hole-doped NdNiO$_2$. This full ab-initio simulation demonstrates the importance of a multi-orbital description, even for the undoped compound, and produces results for the resistivity and Hall conductance in qualitative agreement with experiment.
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