Derivation and numerical study of the singlet-triplet model for cuprate superconductors

M. E. Simón; A. A. Aligia

doi:10.1103/PhysRevB.52.7701

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Derivation and numerical study of the singlet-triplet model for cuprate superconductors

M. E. Simón, A. A. Aligia

DOI 10.1103/PhysRevB.52.7701 · Physical Review B

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Abstract

We perform a low-energy reduction of the three-band Hubbard Hamiltonian (H3b), keeping in the relevant Hilbert subspace not only local singlets (Zhang-Rice singlets), but also triplet states between Cu holes and O holes at the Wannier function of the same site, with x2-y2 symmetry. We solve exactly the resulting Hamiltonian HT in a system of 2×2 unit cells. From the analytical dependence of the parameters of HT and the numerical results, one can see that the local triplet states can be practically neglected for finite O-Cu on-site energy difference Δ, very large Cu on-site Coulomb repulsion Ud, and O-O hopping tpp=0. This fact is in contrast with the mapping of H3b to a one-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 increases with tpp and for large tpp it is necessary to introduce higher-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 describe the lowest-energy levels. We also discuss briefly the effect of nonbonding O orbitals.