Correlation effects in a simplified bilayer two-orbital Hubbard model at half filling

Motivated by the discovery of high-temperature superconductivity in bilayer nickelate ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ under pressure, we investigate the ground-state phase diagram and correlation effects using determinant quantum Monte Carlo simulations in a simplified bilayer two-orbital Hubbard model at half filling. Our results reveal the emergence of a nonmagnetic weakly insulating phase at weak on-site Hubbard interactions, transitioning to an antiferromagnetic Mott insulating phase as the interaction strength exceeds a critical value $U/{t}_{1}^{x}\ensuremath{\approx}4.15$. This phase transition is consistent with the 3D O(3) Heisenberg universality class. Additionally, we analyze dynamical properties such as the single-particle spectral function and dynamic spin structure factor. The pronounced interlayer correlation of ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbitals results in a downward trend and an extended flatness in the $\ensuremath{\gamma}$ band, mirroring the angle-resolved photoemission spectroscopy findings under ambient pressure. Our numerical results provide important clues for understanding the strong correlation effects in ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$.