Generalized spin density wave state of the Hubbard model on the C12 and C60 clusters

Abstract

The one-band Hubbard model at half-filling on a truncated tetrahedron (C${}_{12}$), and on the C${}_{60}$ molecule is studied. Within the Hartree-Fock approximation, we find a magnetic-like instability of the `Fermi sea' towards a spin-ordered phase for an intermediate value of the coupling $(U/t{)}_{\mathrm{c}}\approx 2.6$. The ordered phase presents a spin arrangement similar to that of the classical Heisenberg model defined on the same clusters. We study the linear excitations around the Hartree-Fock ground states using the random-phase approximation. On a finite cluster, we expect that these results signal the presence of a $rapid$ $crossover$ between a paramagnetic region and a regime where spin correlations are important. The relationship with the Heisenberg limit (large $U/t$) is discussed. Finally, we comment on implications of our results for purely repulsive models of superconductivity in alkali-metal-doped fullerenes.

13 pages, plain TeX, 3figs not included