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A comparative study is made on the metal-insulator transition of Diracfermions in the honeycomb and \pi-flux Hubbard models at half filling by meansof the variational cluster approximation and cluster dynamical impurityapproximation. Paying particular attention to the choice of the geometry ofsolver clusters and the inclusion of particle-bath sites, we show that thedirect transition from the Dirac semimetallic state to the antiferromagneticMott insulator state occurs in these models, and therefore, the spin liquidphase is absent in the intermediate region, in agreement with recentquantum-Monte-Carlo--based calculations.

Metal-Insulator Transition of Dirac Fermions: Variational Cluster Study