  We have studied the ground state of the half-filled Hubbard model on a
honeycomb lattice by performing the cluster dynamical mean field theory
calculations with exact diagonalization on the cluster-impurity solver. Through
using elaborate numerical analytic continuation, we identify the existence of a
`spin liquid' from the on-site interaction U=0 to $U_c$ (between $4.6t$ and
$4.85t$) with a smooth crossover correspondingly from the charge fluctuation
dominating phase into the charge correlation dominating phase. The
semi-metallic state exits only at U=0. We further find that the magnetic phase
transition at $U_c$ from the `spin liquid' to the N\'{e}el antiferromagnetic
Mott insulating phase is a first-order quantum phase transition. We also show
that the charge fluctuation plays a substantial role on keeping the `spin
liquid' phase against the emergence of a magnetic order.
