Small-bandwidth perturbation theory for highly covalent Mott insulators

Abstract

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.