Dilemmas in the Choice of Model Spaces Supporting Magnetic Hamiltonians

Abstract

Heisenberg Hamiltonians⁽¹⁾ were first introduced as phenomenological Hamiltonians to reproduce the energy splittings between the electronic states of polyradical systems, i.e. in problems involving several unpaired electrons. The foundation of such Hamiltonians has been clearly established as effective Hamiltonians ^(2–8), in the sense of Quasi Degenerate Perturbation Theory^(9–10), concerning special types of problems and a special choice of the model space ^(11). The concerned systems are half-filled band problems namely, pn e^- in pn atomic (or local) degenerate orbitals (AO), on n centers. The band must be unique and half-filled since one might put up to 2np e⁻ in pn orbitals. The model space is uniquely defined as spanned by all the determinants in which each AO bears one and only one electron, which means that all the determinants have the same space part; then the unique degree of freedom in the spin distribution and the effective hamiltonian must be a spin-only Hamiltonian. The first purpose of this paper is to discuss the choice of that model space, showing that even for half-filled bands it lacks generality and faces numerous fundamental problems.