Effective single-band models for the high-T-c cuprates .1. Coulomb interactions

Starting with the three-band extended Hubbard model (or d-p model) widely used to represent the CuO2 planes in the high-T-c cuprates, we make a systematic reduction to an effective single-band model using a previously developed cell-perturbation method. The range of parameters for which this mapping is a good approximation is explored in the full Zaanen-Sawatzky-Allen diagram (copper Coulomb repulsion U-d versus charge-transfer energy epsilon), together with an investigation of the validity of a further mapping to an effective charge-spin (t-J-V) model. The variation of the effective single-band parameters with the parameters of the underlying multi-hand model is investigated in detail, and the parameter regime where the model represents the high-T-c cuprates is examined for specific features that might distinguish it from the general case. In particular, we consider the effect of Coulomb repulsions on oxygen (U-p) and between copper and oxygen (V-pd) We find that the reduction to an effective single-band model is generally valid for describing the low-energy physics, and that V-pd and U-p (unless unrealistically large) actually slightly improve the convergence of the cell-and perturbation method. Unlike in the usual single-band Hubbard model, the effective intercell hopping and Coulomb interactions are different for electrons and holes. We find that this asymmetry, which vanishes in the extreme Mott-Hubbard regime (U-d much less than epsilon), is quite appreciable in the charge-transfer regime (U-d epsilon), particularly for the effective Coulomb interactions, We show that for doped holes (forming Zhang-Rice singlets) on neighboring cells the interaction induced by V-pd can even be attractive due to locally enhanced pd hybridization, while this cannot occur for electrons. The Coulomb interaction induced by U-p is always repulsive; in addition U-p gives rise to a ferromagnetic spin-spin interaction which opposes antiferromagnetic superexchange. We show that for hole-doped systems this leads to a subtle cancellation of attractive and repulsive contributions, due to antiferromagnetic and charge-polarization effects, to the net static interaction in a charge-spin (t-J-V) model, and We discuss the significance of this result. The asymmetry in the ee, hh, and eh effective hopping parameters can be particularly large for next-nearest neighbors. Specializing to cuprate parameters, we find that the asymmetry in the nearest-neighbor hopping parameters almost vanishes (accidentally), while the next-nearest-neighbor hopping parameter t' is close to zero for electrons but is appreciable for holes (t' approximate to -0.06 eV). The effective Coulomb interaction between doped holes is found to be repulsive, and even slightly larger than for electrons. All the underlying d-p parameters make significant contributions to the effective interactions and it is shown that certain approximations, such as U-d = infinity and t(pp) = 0, can be qualitatively incorrect.