  Building upon the recent progress on the intriguing underlying physics for
the newly discovered infinite-layer nickelates, in this article we review an
examination of valence charge and spin excitations via multi-orbital Hubbard
models as way to determine the fundamental building blocks for Hamiltonians
that can describe the low energy properties of infinite-layer nickelates. We
summarize key results from density-functional approaches, and apply them to the
study of x-ray absorption to determine the valence ground states of
infinite-layer nickelates in their parent form, and show that a fundamental
$d^9$ configuration as in the cuprates is incompatible with a self-doped ground
state having holes in both $d_{x^2-y^2}$ and a rare-earth-derived axial
orbital. When doped, we determine that the rare-earth-derived orbitals empty
and additional holes form low spin $(S=0)$ $d^8$ Ni states, which can be
well-described as a doped single-band Hubbard model. Using exact
diagonalization for a 2-orbital model involving Ni and rare earth orbitals, we
find clear magnons at 1/2 filling that persist when doped, albeit with larger
damping, and with a dependence on the precise orbital energy separation between
the Ni- and rare-earth-derived orbitals. Taken together, a full two-band model
for infinite-layer nickelates can well describe the valence charge and spin
excitations observed experimentally.
