Comparison of effective models forCuO2layers in oxide superconductors

Several effective models, as derived from a general two-band Hubbard model for ${\mathrm{CuO}}_2$ layers in oxide superconductors, are studied. In particular, we compare the Hubbard model with the hole-spin models (unsymmetrized and symmetrized) and a generalized effective single-band (t-J) model. The exact calculation of energy spectra on a chain of four cells shows that states for a single additional hole are quite well reproduced by reduced models, taking into account the renormalization of constants. Less satisfactory is the agreement for the undoped system, especially for small charge-transfer energies. The same analytical procedure is applied to the square lattice system, where the parameters are estimated also from the levels of a single ${\mathrm{CuO}}_4$ group. The results for quasiparticle spectra indicate that corrections to the t-J model are even smaller than in the case of the single-band Hubbard model.