Calculation of the elastic neutron scattering form factor by an essentially standard approach has given results that disagree seriously with experiment on ${\mathrm{La}}_2{\mathrm{NiO}}_4.$ This has motivated us to look for a more fundamental approach to such a calculation (in Mott insulators). We have begun by considering perturbation approaches in the context of the three-band Hubbard model of cuprate ${\mathrm{CuO}}_2$ planes due to Hybertsen et al. This was recently shown, for a small cluster, to have a straightforward small-bandwidth perturbation expansion of the Heisenberg exchange parameter $J$ that is nonconvergent. We study the roles of one-body and two-body transformations on the basis set of states in converting nonconvergent many-body perturbation expansions into convergent ones. We choose the one-body transformations guided by the thermal single determinant approximation (TSDA), a variational generalization of the thermal Hartree-Fock approximation. All transformations preserve “localization” of copper $d$ orbitals, and thus lead to low-lying states governed by a Heisenberg spin Hamiltonian, in leading order, provided the perturbation theory is convergent. We find the one-body transformations do make the perturbation expansion converge, although rather slowly; addition of two-body transformations gives significant improvement in the convergence rate. The reason for the limitation of the one-body transformation is given.

• Received 13 June 1997

DOI:https://doi.org/10.1103/PhysRevB.56.15596