Dynamics of holes in the extended Hubbard model

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Abstract
The strong-correlation limit of the extended Hubbard model of plane cuprate perovskites is considered for two ratios of material parameters allowed by the uncertainty of their known values: the Cu-O electron promotion energy is of the order of the Cu-O hybridization at a negligibly small Hubbard repulsion on oxygen sites and the hybridization is much smaller than other energy parameters. By taking into account the antiferromagnetic ordering of lightly doped samples and using the spin-wave approximation, for these two cases effective Hamiltonians are obtained, in which charge and spin degrees of freedom are described by practically independent operators. On the basis of these Hamiltonians it is shown that the low-energy hole dynamics is essentially different in the two cases. In the latter case it can approximately be mapped on the one-band t-J model describing the movement of the Zhang-Rice singlet. However, essential deviations might arise if the oxygen and copper on-site repulsions were comparable. The Hamiltonian in the former case is intrinsically a two-band one which differs from the one-band Hamiltonian in shapes and widths of energy bands and in conditions of the formation of a ferromagnetically ordered region around a hole in the limit of large repulsions.