The effective Hamiltonian for cuprates at different energy scales

Abstract A multiband p−d model describes electronic properties of cuprates in the large energy scale ∼ U ∼10 eV. In the strong electron correlation (SEC) limit we project out double occupied intra-atomic states and obtain the singlet–triplet t - t ′ - t ″ - J * model at scale ∼ Ω ≈ 0.5 eV , where Ω is the excitation energy between two-hole singlet and triplet states. At smaller energies ∼ J one gets the usual t - t ′ - t ″ - J * model. At energies ∼ ω D one has to add electron–phonon interaction, and the low-energy effective Hamiltonian with magnetic and phonon mechanisms of pairing is constructed in SEC limit with parameters calculated from the ab initio approach. Magnetic mechanism of pairing results in a very high value of the critical temperature T c while electron–phonon interaction suppresses d-pairing to the T c ∼100 K.