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We extend the methods recently introduced in Phys. Rev. Lett. 106 036401(2011) to investigate correlations between two spin-polarons in aquasi-two-dimensional CuO2 layer. The low-energy wavefunctions for two dopedholes introduced in a half-filled CuO2 plane with 32 copper and 64 oxygen sitesare calculated explicitly using an efficient yet accurate truncation scheme tomodel the antiferromagnet background. The energetics and wavefucntions showthat the charges form three-spin polarons and the spin is carried by adisturbance around the three-spin polaron core. The low-energy band resultsfrom the competition between the kinetic energy and a local attractivepotential which favors d(x^2-y^2) states. Lastly, we point out features thatare expected to be robust for larger systems.

A computational approach to a doped antiferromagnet: correlations between two spin-polarons in the lightly doped CuO$_2$ plane