  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.
