  We extend the methods recently introduced in Phys. Rev. Lett. 106 036401
(2011) to investigate correlations between two spin-polarons in a
quasi-two-dimensional CuO2 layer. The low-energy wavefunctions for two doped
holes introduced in a half-filled CuO2 plane with 32 copper and 64 oxygen sites
are calculated explicitly using an efficient yet accurate truncation scheme to
model the antiferromagnet background. The energetics and wavefucntions show
that the charges form three-spin polarons and the spin is carried by a
disturbance around the three-spin polaron core. The low-energy band results
from the competition between the kinetic energy and a local attractive
potential which favors d(x^2-y^2) states. Lastly, we point out features that
are expected to be robust for larger systems.
