Generalized spin-density-wave state of the Hubbard model for ${\mathrm{C}}_{12}$ and ${\mathrm{C}}_{60}$ clusters

The one-band Hubbard model at half filling on a truncated tetrahedron (${\mathrm{C}}_{12}$) and on the ${\mathrm{C}}_{60}$ molecule is studied. Within the Hartree-Fock approximation, we find a magneticlike instability of the ‘‘Fermi sea’’ towards a spin-ordered phase for an intermediate value of the coupling (U/t${)}_{\mathit{c}}$≊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.