Interplay between Hubbard interaction and charge transfer energy in the three-orbital Emery model: Implications for cuprates and nickelates

We use the numerically unbiased determinant quantum Monte Carlo method to systematically investigate the three-orbital Emery model in the normal state in a wide range of local interactions, charge transfer energy, and doping levels. We focus on the influence of the on-site Hubbard ${U}_{dd}$ and the charge transfer energy scale ${\ensuremath{\epsilon}}_{p}$ on the electronic properties via the orbital occupancies, local moments, spin correlations, and spectral properties. Rich features of the orbital-resolved local and momentum-dependent spectra are revealed to be associated with the possible Zhang-Rice singlet breakdown reflected by the peak splitting near the Fermi level in the heavily overdoped regime. Moreover, the pseudogap features at a small charge transfer energy scale (relevant to cuprates) are shown to diminish at larger ${\ensuremath{\epsilon}}_{p}$, which implies the weakening or absence of the pseudogap in the infinite-layer nickelates. Besides, an optimal value of ${\ensuremath{\epsilon}}_{p}$ is identified for maximizing the antiferromagnetic spin correlations. Our large-scale simulations provide additional insights into the well-established Emery model, particularly in the regime of heavily overdoped and/or large charge transfer energy scale.