  The unique linear density of state around the Dirac points for the honeycomb
lattice brings much novel features in strongly correlated models. Here we study
the ground-state phase diagram of the Kondo lattice model on the honeycomb
lattice at half-filling by using an extended mean-field theory. By treating
magnetic interaction and Kondo screening on an equal footing, it is found that
besides a trivial discontinuous first-order quantum phase transition between
well-defined Kondo insulator and antiferromagnetic insulating state, there can
exist a wide coexistence region with both Kondo screening and antiferromagnetic
orders in the intermediate coupling regime. In addition, the stability of Kondo
insulator requires a minimum strength of the Kondo coupling. These features are
attributed to the linear density of state, which are absent in the square
lattice. Furthermore, fluctuation effect beyond the mean-field decoupling is
analyzed and the corresponding antiferromagnetic spin-density-wave transition
falls into the O(3) universal class. Comparatively, we also discuss the Kondo
necklace and the Kane-Mele-Kondo (KMK) lattice models on the same lattice.
Interestingly, it is found that the topological insulating state is unstable to
the usual antiferromagnetic ordered states at half-filling for the KMK model.
The present work may be helpful for further studies on the interplay between
conduction electrons and the densely localized spins on the honeycomb lattice.
