Using the determinant Quantum Monte Carlo method, we investigate the interplay among doping, interlayer tunneling, and on-site Hund's coupling in stabilizing superconductivity (SC) in a two-orbital model for the bilayer nickelate ${\text{La}}_3{\text{Ni}}_2{\text{O}}_7$. With realistic dispersion and for certain values of the interaction parameters, the auxiliary-field-decoupled fermion Hamiltonian has Kramers antiunitary symmetries which guarantee the absence of a sign problem. The same antiunitary symmetries can also be used to show there is a second instability towards the $(\pi ,\pi )$ interlayer bond order (BO) in the strong interaction limit. We indicate the possible connection between this bond order and the enigmatic density wave state observed in experiments and clarify the decisive role played by the interlayer tunneling in the competition between the SC and the BO. Finally, possible directions on how to enhance the SC transition temperature and stabilize the SC phase are also discussed.

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• Superconductivity
• Strongly correlated systems
• Electron-correlation calculations
• Materials modeling
• Quantum Monte Carlo