Me. Simon et Aa. Aligia, DERIVATION AND NUMERICAL STUDY OF THE SINGLET-TRIPLET MODEL FOR CUPRATE SUPERCONDUCTORS, Physical review. B, Condensed matter, 52(10), 1995, pp. 7701-7707
We perform a low-energy reduction of the three-band Hubbard Hamiltonia
n (H-3b), keeping in the relevant Hilbert subspace not only local sing
lets (Zhang-Rice singlets), but also triplet states between Cu holes a
nd O holes at the Wannier function of the same site, with x(2)-y(2) sy
mmetry. We solve exactly the resulting Hamiltonian H-T in a system of
2 x 2 unit cells. From the analytical dependence of the parameters of
H-T and the numerical results, one can see that the local triplet stat
es can be practically neglected for finite O-Cu on-site energy differe
nce Delta, very large Cu on-site Coulomb repulsion U-d, and O-O hoppin
g t(pp) = 0. This fact is in contrast with the mapping of H-3b to a on
e-band model using nonorthogonal singlets, which is very accurate when
the Cu+ configuration can be neglected. Although the amount of local
triplet states in the low-energy eigenstates is in general small, it i
ncreases with t(pp) and for large t(pp) it is necessary to introduce h
igher-order corrections in the one-band model to accurately represent
the low-energy physics. In all cases even when local triplets are not
important, the t-J model should be supplemented with other terms, to d
escribe the lowest-energy levels. We also discuss briefly the effect o
f nonbonding O orbitals.