  Quantum phase transitions in the Hubbard model on the honeycomb lattice are
investigated in the variational cluster approximation. The critical interaction
for the paramagnetic to antiferromagnetic phase transition is found to be in
remarkable agreement with a recent large-scale quantum Monte Carlo simulation.
Calculated staggered magnetization increases continuously with $U$ and thus we
find the phase transition is of a second order. We also find that the
semimetal-insulator transition occurs at infinitesimally small interaction and
thus a paramagnetic insulating state appears in a wide interaction range. A
crossover behavior of electrons from itinerant to localized character found in
the calculated single-particle excitation spectra and short-range spin
correlation functions indicates that an effective spin model for the
paramagnetic insulating phase is far from a simple Heisenberg model with a
nearest-neighbor exchange interaction.
