▎ 摘　　要

We apply quantum Monte Carlo technique to address the issue of high controllability of ferromagnetism in graphene and the issue of electron correlation driven superconductivity in graphene, by simulating the t - U - V Hubbard model on a honeycomb lattice. In the region of low electron band filling below the Van Hove singularity, the system shows a short-range ferromagnetic correlation, which is strengthened slightly by the on-site Coulomb interaction and markedly by the next nearest-neighbor hoping integral. The strong dependence of ferromagnetism on the electron band filling can be manipulated by applying electric gate voltage. For V=0 and close to the half filling, we find that pairing with d + id symmetry dominates pairing with extended-s symmetry. However, as the system size increases the long-range part of the d + id pairing correlation decreases and tends to vanish in the thermodynamic limit. An inclusion of nearest-neighbor interaction V, either repulsive or attractive, has a small effect on the extended-s pairing correlation, but strongly suppresses the d + id pairing correlation. Copyright (C) 2013 John Wiley & Sons, Ltd.