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Using \emph{ab initio} band structure and DFT+dynamical mean-field theorymethods we examine the effects of electron-electron interactions on the normalstate electronic structure, Fermi surface, and magnetic correlations of therecently discovered double-layer perovskite superconductor La$_3$Ni$_2$O$_7$under pressure. Our results suggest the formation of a negative charge transfermixed-valence state with the Ni valence close to 1.75+. We find a remarkableorbital-selective renormalization of the Ni $3d$ bands, with $m^*/m \sim 3$ and2.3 for the Ni $3z^2-r^2$ and $x^2-y^2$ orbitals, respectively, in agreementwith experimental estimates. Our results for the {\bf k}-dependent spectralfunctions and Fermi surfaces show significant incoherence of the Ni $3z^2-r^2$states, implying the proximity of the Ni $3d$ states to orbital-dependentlocalization. Our analysis of the static magnetic susceptibility suggests thepossible formation of the spin and charge (or bond) density wave stripe states.

Correlated electronic structure, orbital-selective behavior, and magnetic correlations in double-layer La$_3$Ni$_2$O$_7$ under pressure