A comparative study is made on the metal-insulator transition of Dirac fermions in the honeycomb and pi-flux Hubbard models at half filling by means of the variational cluster approximation and cluster dynamical impurity approximation. Paying particu
lar attention to the choice of the geometry of solver clusters and the inclusion of particle-bath sites, we show that the direct transition from the Dirac semimetallic state to the antiferromagnetic Mott insulator state occurs in these models, and therefore, the spin liquid phase is absent in the intermediate region, in agreement with recent quantum-Monte-Carlo--based calculations.
