Quasiparticles in the copper-oxygen planes of high-$T_c$ superconductors: An exact solution for a ferromagnetic background

A model for a mobile hole in the copper oxide planes of high-temperature superconductors is solved exactly. The hole moves on the oxygen atoms through a lattice of spins localized on the copper atoms. In order to obtain a solvable problem, it is assumed that the copper atoms provide a ferromagnetic background. The resulting quasiparticles have both charge and spin in contrast to the Cu-O singlets occurring in proposed effective single-band Hubbard models derived from the Cu-O network. Thus these two models of high-temperature superconductors may have different low-energy physics.