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

The diamagnetic susceptibility chi of half-filled fermion models with N = 4 n + 2 sites is related to chemical shifts in molecules and charge stiffness in extended systems. The slow evolution of chi( N) with N in Hubbard model s or spinless fermions indicates a small energy gap, as known from exact so lutions of regular chains. A gap due to alternating transfer integrals (1 /- delta) suppresses chi for N delta > 1, but is a small correction for N d elta<1. Exact ring currents N chi of Pariser-Parr-Pople (PPP) and Hubbard m odels are extended to N = 18 in D-18h symmetry. Hydrocarbon PPP parameters account for the anisotropy of proton shifts in 14 and 18 annulenes, for sma ller shifts at larger N, and for larger shifts of anions with 4n + 2 pi-ele ctrons. Fermion models with arbitrary spin-independent interactions are sho wn to have vanishing chi for open boundary conditions (chains) at half fill ing or finite N. Diamagnetic currents in molecules require rings but are no t sensitive to small bond-length variations, while an energy gap rather tha n topology enters in the charge stiffness of extended systems. Although for mally identical, chi has different applications in finite and extended syst ems and its convergence with N can be rapid or very slow. Spin-charge separ ation reflects correlations rather than topology in half-filled Hubbard, PP P, and spinless fermion models; 4n and 4n + 2 rings with oppositely signed chi show similar spin-charge separation with increasing correlations. (C) 2 000 American Institute of Physics. [S0021-9606(00)51007-1].