  Using the variational cluster approximation (VCA) and the cluster
perturbation theory, we study the finite temperature phase diagram of a
half-depleted periodic Anderson model on the honeycomb lattice at half filling
for a model of graphone, i.e., single-side hydrogenated graphene. The ground
state of this model is found to be ferromagnetic (FM) semi-metal. The spin wave
dispersion in the FM state is linear in momentum at zero temperature but
becomes quadratic at finite temperatures, implying that the FM state is fragile
against thermal fluctuations. Indeed, our VCA calculations find that the
paramagnetic (PM) state dominates the finite temperature phase diagram. More
surprisingly, we find that massless Dirac quasiparticles with the linear energy
dispersion emerge at the Fermi energy upon introducing the electron correlation
$U$ at the impurity sites in the PM phase. The Dirac Fermi velocity is found to
be highly correlated to the quasiparticle weight of the emergent massless Dirac
quasiparticles at the Fermi energy and monotonically increases with $U$. These
unexpected massless Dirac quasiparticles are also examined with the Hubbard-I
approximation and the origin is discussed in terms of the spectral weight
redistribution involving a large energy scale of $U$. Considering an effective
quasiparticle Hamiltonian which reproduces the single-particle excitations
obtained by the Hubbard-I approximation, we argue that the massless Dirac
quasiparticles are protected by the electron correlation. Our finding is
therefore the first example of the emergence of massless Dirac quasiparticles
due to dynamical electron correlations without breaking any spatial symmetry.
The experimental implications of our results for graphone as well as a graphene
sheet on transition metal substrates are also briefly discussed.
