Ring currents and charge stiffness in molecular and extended models of interacting fermions

Abstract

The diamagnetic susceptibility χ of half-filled fermion models with N=4n+2 sites is related to chemical shifts in molecules and charge stiffness in extended systems. The slow evolution of χ(N) with N in Hubbard models or spinless fermions indicates a small energy gap, as known from exact solutions of regular chains. A gap due to alternating transfer integrals (1±δ) suppresses χ for Nδ>1, but is a small correction for Nδ<1. Exact ring currents Nχ of Pariser–Parr–Pople (PPP) and Hubbard models are extended to N=18 in D18h symmetry. Hydrocarbon PPP parameters account for the anisotropy of proton shifts in 14 and 18 annulenes, for smaller shifts at larger N, and for larger shifts of anions with 4n+2 π-electrons. Fermion models with arbitrary spin-independent interactions are shown to have vanishing χ for open boundary conditions (chains) at half filling or finite N. Diamagnetic currents in molecules require rings but are not sensitive to small bond-length variations, while an energy gap rather than topology enters in the charge stiffness of extended systems. Although formally identical, χ has different applications in finite and extended systems and its convergence with N can be rapid or very slow. Spin–charge separation reflects correlations rather than topology in half-filled Hubbard, PPP, and spinless fermion models; 4n and 4n+2 rings with oppositely signed χ show similar spin–charge separation with increasing correlations.