Strong coupling models for the electronic structure of La2CuO4 are derived in two successive stages of renormalization. First, a three-band Hubbard model is derived using a constrained density functional approach. Second, exact diagonalization studies of finite clusters within the three band Hubbard model are used to select and map the low energy spectra onto effective one-band Hamiltonians. At each stage, some observables are calculated and found to be in quantitative agreement with experiment. The final results suggest the following models to be adequate descriptions of the low energy scale dynamics: (1) a spin 1/2 Heisenberg model for the insulating case with nearest neighbor J≈130 meV; (2) a "t–t’–J" model with nearly identical parameters for the electron and hole doped cases.
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The singlet is treated as a doubly occupied site for sign purposes. If it is treated as a vacancy in the “t—t’—J” model instead, then the signs of t, t ‘ are reversed from Eq. (3) for the hole case.
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Hybertsen, M.S., Schluter, M., Stechel, E.B. et al. Renormalization from Density Functional Theory to Strong Coupling Models for the Electronic Structure of La2CuO4. MRS Online Proceedings Library 169, 19–22 (1989). https://doi.org/10.1557/PROC-169-19