  Recently, a bulk nickelate superconductor $\mathrm{La_3Ni_2O_7}$ is
discovered at pressures with a remarkable high transition temperature $T_c \sim
80K$. Here, we study a Hubbard model with tight-binding parameters derived from
\textit{ab initio} calculations of $\mathrm{La_3Ni_2O_7}$, by employing large
scale determinant quantum Monte Carlo and cellular dynamical mean-field theory.
Our result suggests that the superexchange couplings in this system are
comparable to that of cuprates. The system is a charge transfer insulator as
hole concentration becomes four per site at large Hubbard $U$. Upon hole
doping, two low-energy spin-singlet bands emerge in the system exhibiting
distinct correlation properties: while the one composed of the out-of-plane
Ni-$d_{3z^2-r^2}$ and O-$p_z$ orbitals demonstrates strong antiferromagnetic
correlations and narrow effective bandwidth, the in-plane singlet band
consisting of the Ni-$d_{x^2-y^2}$ and O-$p_x / p_y$ orbitals is in general
more itinerant. Over a broad range of hole doping, the doped holes occupy
primarily the $d_{x^2-y^2}$ and $p_x / p_y$ orbitals, whereas the
$d_{3z^2-r^2}$ and $p_z$ orbitals retain underdoped. We propose an effective $
t-J$ model to capture the relevant physics and discuss the implications of our
result for comprehending the $\mathrm{La_3Ni_2O_7}$ superconductivity.
