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Building upon the recent progress on the intriguing underlying physics forthe newly discovered infinite-layer nickelates, in this article we review anexamination of valence charge and spin excitations via multi-orbital Hubbardmodels as way to determine the fundamental building blocks for Hamiltoniansthat can describe the low energy properties of infinite-layer nickelates. Wesummarize key results from density-functional approaches, and apply them to thestudy of x-ray absorption to determine the valence ground states ofinfinite-layer nickelates in their parent form, and show that a fundamental$d^9$ configuration as in the cuprates is incompatible with a self-doped groundstate having holes in both $d_{x^2-y^2}$ and a rare-earth-derived axialorbital. When doped, we determine that the rare-earth-derived orbitals emptyand additional holes form low spin $(S=0)$ $d^8$ Ni states, which can bewell-described as a doped single-band Hubbard model. Using exactdiagonalization for a 2-orbital model involving Ni and rare earth orbitals, wefind clear magnons at 1/2 filling that persist when doped, albeit with largerdamping, and with a dependence on the precise orbital energy separation betweenthe Ni- and rare-earth-derived orbitals. Taken together, a full two-band modelfor infinite-layer nickelates can well describe the valence charge and spinexcitations observed experimentally.

On the nature of valence charge and spin excitations via multi-orbital Hubbard models for infinite-layer nickelates