A study of the magnetic properties in the Hubbard model on the honeycomb lattice by variational cluster approximation

Magnetic properties of the half-filled Hubbard model on the honeycomb lattice, which is a simple model of graphene, are studied using the variational cluster approximation (VCA). We found that the critical interaction strength of a magnetic transition is slightly lower than that of the nonmagnetic metal-to-insulator transition and the magnetic order parameter is already nonnegligible at the latter transition point. Thus, a semi-metallic state becomes a magnetic insulator as the interaction strength increases, and a spin liquid state characterized by a Mott insulator without spontaneously broken spatial or spin symmetry, or a state very close to that is not realized in this system. Both the magnetic and nonmagnetic metal-to-insulator transitions are of the second-order. Our results agree with recent large scale quantum Monte Carlo (QMC) simulations.