Abstract

Starting with a five-band Hubbard model, we make a systematic reduction to an effective single-band Hubbard model using a previously developed cell-perturbation method. Particular emphasis is given to the effect of apical oxygen ions. It is shown that for the parameter range corresponding to the cuprates there is, in addition to the usual Zhang-Rice singlet, a two-hole cell state which can be low in energy and depends sensitively on the proximity of the apicals. The potential significance of this state is discussed. We show that for the parameter regime where the system may be reduced to a t- t′- J model, the main effect is to renormalise significantly the next-nearest-neighbour hopping ( t′), having negligible effect on t and J. The parameter regime for which such a mapping breaks down is discussed together with the possible breakdown of the effective single-band model itself.

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