SYSTEMATIC DERIVATION OF A GENERALIZED T-J MODEL

We perform a consistent low-energy reduction of the three-band Hubbard model H-3b to an effective one-band model H-1b, using as an intermediate step a renormalized effective spin-fermion model H(sf) in which Cu+ and Cu3+ configurations are contained as virtual states. We map PH(sf)P into H-1b using two projectors P onto different Zhang-Rice singlets: (1) orthogonal singlets constructed using O Wannier functions, (2) nonorthogonal singlets. In case, 1 (2) the mapping is almost exact (exact as shown before by Zhang) if direct, O-O hopping and the Cu3+ (Cu+) configuration can be neglected.