Ground-state properties of the Hubbard model on a ${\mathrm{C}}_{60}$ cluster

Using quantum Monte Carlo techniques, we study the one-band Hubbard model at half filling, on a ${\mathrm{C}}_{60}$ molecule. Spin-spin correlations are measured at couplings U/t=4 and 8, and results are compared with similar studies on square lattices. At the lowest temperatures accessible to our simulations, we find that the spin correlations on the ${\mathrm{C}}_{60}$ molecule tend to vanish at large distances, with a correlation length of 3–4 lattice spacings. Spin-wave calculations in the Heisenberg limit are also reported, in qualitative agreement with Monte Carlo simulations. These results suggest that the ground state of the half-filled Hubbard model on the ${\mathrm{C}}_{60}$ fullerene is spin disordered (defined as having a correlation length smaller than the cluster size), in contrast with the spin-density-wave state that exists on the two-dimensional square lattice. We believe that a ‘‘dimer’’ state may properly describe the undoped ${\mathrm{C}}_{60}$ molecule.