A possibility of the electronic origin of the high-temperature superconductivity in cuprates is probed with the quantum Monte Carlo method by revisiting the three-band Hubbard model comprising Cu ${3d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ and O ${2p}_{\ensuremath{\sigma}}$ orbitals. The ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ pairing correlation is found to turn into an increasing function of the repulsion
Ud within the
d orbitals or the
d-
p level offset $\ensuremath{\Delta}\ensuremath{\varepsilon}$, where the normalized correlation grows with the system size. We have detected this in both the charge-transfer and Mott-Hubbard regimes upon entering the strong-correlation region (
Ud or $\ensuremath{\Delta}\ensuremath{\varepsilon}>$ bare bandwidth).
Understanding the physics underlying high-temperature superconductivity in cuprates and, more recently, infinite-layer nickelates has remained a central challenge in condensed-matter physics. We establish neural quantum states (NQS), specifically Hidden Fermion Determinant States (HFDS), as a scalable variational approach to the three-band Emery model of the copper- and nickel-oxide layers in these materials. After benchmarking HFDS against matrix product states on width-two geometries, we study ground states of fully two-dimensional (2D) systems of up to
10×10 unit cells (
300 sites). We characterize the momentum-space distribution of dopants and find a pronounced electron-hole dichotomy similar to cuprate experiments. We further downfold the three-band model to effective single-band descriptions by constructing interacting Wannier functions. We consider a wide range of parameters -- from the charge-transfer regime relevant to cuprates to the Hubbard-Mott regime of nickelates, as well as systematic scans of the charge-transfer gap that has been demonstrated to impact the critical superconducting temperatures. Across all regimes, the effective model significantly deviates from the usual Fermi-Hubbard model: The typical ratio
U/t is enhanced, some parameters experience a significant doping dependence, and sizable terms beyond the conventional Hubbard model are present, most notably a density-assisted hopping
tn. Notably, in all effective models,
tn has the largest contribution to particle-hole asymmetry, rather than next-nearest-neighbor hopping contributions. The effective parameters sensitively depend on the charge-transfer energy, doping, and interaction ratios. Our results establish HFDS as an efficient tool for studying the 2D Emery model and demonstrate that single-band descriptions can require interaction terms generated by the underlying multi-band models.
Abstract We investigate the doping evolution of the electronic state of the three-band t-J-U model considering the normal state of the hole-doped high- T c superconducting cuprate. In our model, when some number of holes are doped into the undoped state, the d electron exhibits the charge-transfer (CT)-type Mott-Hubbard transition along with a chemical potential jump. A reduced CT gap is formed from the p band and the coherent component of the d band, and it shrinks due to charge fluctuations as more holes are doped as in the pseudogap (PG) phenomenon. This trend is reinforced as the d-p band hybridization is increased, and a Fermi liquid state is retrieved as in the Kondo effect. These suggest that the PG in the hole-doped cuprate emerges due to the CT transition and the Kondo effect.