Mott-Hubbard transition and antiferromagnetism on the honeycomb lattice

The Hubbard model is investigated for a half-filled honeycomb lattice, using a variational method. Two trial wave functions are introduced, the Gutzwiller wave function, well suited for describing the ''metallic'' phase at small Ti and a complementary wave function for the insulating regime at large values of U. The comparison of the two variational ground states at the mean-field level yields a Mott transition at U-c/t approximate to 5.3. In addition, a variational Monte Carlo calculation is performed in order to locate the instability of the ''metallic'' wave function with respect to antiferromagnetism. The critical value U-m/t approximate to 3.7 obtained in this way is considered to be a lower bound for the true critical point for antiferromagnetism, whereas there are good arguments that the mean-field value U-c/t approximate to 5.3 represents an upper bound for the Mott transition. Therefore the ''metal''-insulator transition for the honeycomb lattice may indeed be simultaneously driven by the antiferromagnetic instability and the Mott phenomenon.