For the calculation of charge excitations as those observed in, e.g., photoemission spectroscopy or in electron-energy-loss spectroscopy, a correct description of ground-state charge properties is essential. In strongly correlated systems like the undoped cuprates this is a highly nontrivial problem. In this paper we derive a nonperturbative analytical approximation for the ground state of the three-band Hubbard model on an infinite, half-filled
CuO2 plane. By comparison with projector quantum Monte Carlo calculations it is shown that the resulting expressions correctly describe the charge properties of the ground state. Relations to other approaches are discussed. The analytical ground state preserves size consistency and can be generalized for other geometries, while still being both easy to interpret and to evaluate.
We simulated the three-band Hubbard model using the constrained-path Monte Carlo (CPMC) method in search for a possible superconducting ground state. The CPMC is a ground-state method that is free of the exponential scaling of computing time with system size. We calculated the binding energy of a pair of holes for systems up to $6\ifmmode\times\else\texttimes\fi{}4$ unit cells. We also studied the pairing correlation functions versus distance for both the
d-wave and extended
s-wave channels in systems up to $6\ifmmode\times\else\texttimes\fi{}6$. We found that holes bind for a wide range of parameters and that the binding increased as the system size is increased. However, the pairing correlation functions decay quickly with distance. For the extended
s channel, we found that as the Coulomb interaction
Ud on the Cu sites is increased, the long-range part of the correlation functions is suppressed and fluctuates around zero. For the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ channel, we found that the correlations decay rapidly with distance towards a small positive value. However, this value becomes smaller as the interaction
Ud or the system size is increased.