  A spin-fermion model that captures the charge-transfer properties of Cu-based
high critical temperature superconductors is introduced and studied via Monte
Carlo simulations. The strong Coulomb repulsion among $d$-electrons in the Cu
orbitals is phenomenologically replaced by an exchange coupling between the
spins of the itinerant electrons and localized spins at the Cu sites, formally
similar to double-exchange models for manganites. This interaction induces a
charge-transfer insulator gap in the undoped case (five electrons per unit
cell). Adding a small antiferromagnetic Heisenberg coupling between localized
spins reinforces the global tendency towards antiferromagnetic order. To
perform numerical calculations the localized spins are considered classical, as
in previous related efforts. In this first study, undoped and doped $8\times 8$
clusters are analyzed in a wide range of temperatures. The numerical results
reproduce experimental features in the one-particle spectral function and the
density-of-states such as $(i)$ the formation of a Zhang-Rice-like band with a
dispersion of order $\sim 0.5$ eV and with rotational symmetry about wavevector
$(\pi/2,\pi/2)$ at the top of the band, and $(ii)$ the opening of a pseudogap
at the chemical potential upon doping. We also observed incipient tendencies
towards spin incommensurability. This simple model offers a formalism
intermediate between standard mean-field approximations, that fail at finite
temperatures in regimes with short-range order, and sophisticated many-body
techniques such as Quantum Monte Carlo, that suffer sign problems.
