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Quantum versus classical polarons in a ferromagnetic CuO$_3$-like chain

We present an exact solution for an itinerant hole added into the oxygen orbitals of a CuO$_{3}$-like ferromagnetic chain. Using the Green's function method, the quantum polarons obtained for the Heisenberg SU(2) interaction between localized Cu spins are compared with the polarons in the Ising chain. We find that magnons with large energy are favorable towards quasiparticle existence, even in the case of relatively modest electron-magnon coupling. We observe two quasiparticle states with dispersion $\sim 2t$ each, which emerge from the incoherent continuum when the exchange coupling $J$ increases. Quantum fluctuations in the spin system modify the incoherent part of the spectrum and change the spectral function qualitatively, beyond the bands derived from the perturbation theory.