Using quantum Monte Carlo techniques, we study the one-band Hubbard model at half filling, on a
C60 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
C60 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
C60 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
C60 molecule.
Abstract The combination of small-cluster exact-diagonalization calculations and the quantum Monte Carlo method is used to examine ferromagnetism in the two-dimensional Hubbard model with a generalized type of hopping. It is found that the long-range hopping with exponentially decaying hopping amplitudes t ij ∼ − q Ri−Rj stabilizes the ferromagnetic state for a wide range of electron interactions U and electron concentrations n > 1. The critical value of the hopping parameter q c above which the ferromagnetic state becomes stable is calculated numerically and the ground-state phase diagram of the model is discussed for physically the most interesting cases.