Polaron States in a CuO Chain

We introduce a one-dimensional model for a CuO chain, with holes and S=1/2 spins localized in $3d_{x²-y²}$ orbitals, and p_σ oxygen orbitals without holes in the ground state. We consider a single hole doped at an oxygen site and study its propagation by spin-flip processes. We develop the Green function method and treat the hole-spin coupling in the self-consistent Born approximation, similar to that successfully used to study polarons in the regular t-J model. We present an analytical solution of the problem and investigate whether the numerical integration is a good approximation to this solution.