ON PERTURBATION-THEORY FOR THE 3-BAND MODEL OF CUPRATES

We raise and discuss the following question. Why does the spectrum for the three-band model of Hybertson, Stechel, Schluter, and Jennison, c laimed not to be approachable by perturbation theory because of rather large hopping integrals compared to site energy differences, follow p recisely what would be expected by low-order perturbation theory? The latter is, for the insulating case, that the low-lying levels are desc ribable by a Heisenberg Hamiltonian with nearest-neighbor interactions plus much smaller next-nearest-neighbor interactions and n-spin terms , n greater than or equal to 4. We first check whether perturbation th eory actually does not converge, treating the hopping and p-d exchange terms as perturbations. For the crystal, we find that the first three terms contributing to the nearest-neighbor exchange coupling J (which are of third, fourth, and fifth order) increase in magnitude, and are not of the same sign, i.e., there is no sign of convergence to this o rder. We also consider the small cluster, Cu2O7, for which we have car ried out the perturbation series to 14th order; there is still no sign of convergence. Thus the nonconvergence of this straightforward pertu rbation theory is convincingly established. Yet the apparent perturbat ive nature of the spectrum suggests the existence of some perturbation theory that does converge. The possibility of a particular transforma tion of the Hamiltonian leading to a convergent perturbation series, t hereby answering the above question, is discussed. (C) 1996 American I nstitute of Physics.