  The effect of Coulomb correlations in the half-filled Hubbard model of the
honeycomb lattice is studied within the dynamical cluster approximation (DCA)
combined with exact diagonalization (ED) and continuous-time quantum Monte
Carlo (QMC). The important difference between this approach and the previously
employed cluster dynamical mean field theory (CDMFT) is that DCA preserves the
translation symmetry of the system, while CDMFT violates this symmetry. As the
Dirac cones of the honeycomb lattice are the consequence of perfect long-range
order, DCA yields semi-metallic behavior at small onsite Coulomb interactions
$U$, whereas CDMFT gives rise to a spurious excitation gap even for very small
$U$. This basic difference between the two cluster approaches is found
regardless of whether ED or QMC is used as the impurity solver. At larger
values of $U$, the lack of translation symmetry becomes less important, so that
the CDMFT reveals a Mott gap, in qualitative agreement with large-scale QMC
calculations. In contrast, the semi-metallic phase obtained in DCA persists
even at $U$ values where CDMFT and large-scale QMC consistently show Mott
insulating behavior.
