The ground state phase diagram of the dimerized spin-1/2 XX honeycomb model
in presence of a transverse magnetic field (TF) is known. With the absence of
the magnetic field, two quantum phases, namely, the N\'eel and the dimerized
phases have been identified. Moreover, canted N\'eel and the paramagnetic (PM)
phases also emerge by applying the magnetic field. In this paper, using two
complementary numerical exact techniques, Lanczos exact diagonalization, and
Density matrix renormalization group (DMRG) methods, we study this model by
focusing on the quantum correlations, the concurrence, and the quantum discord
(QD) among nearest-neighbor spins. We show that the quantum correlations can
capture the position of the quantum critical points in the whole range of the
ground state phase diagram consistent with previous results. Although the
concurrence and the QD are short-range, informative about long-ranged critical
correlations. In addition, we address a "magnetic-entanglement" behavior that
starts from an entangled field around the saturation field.Comment: 8 pages, 5 figure