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 Néel and the dimerized phases have been identified. Moreover, canted Néel and the paramagnetic (PM) phases also emerge by applying the magnetic field. In this paper, using two powerful 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.

We consider the spin-1/2 XY frustrated antiferromagnetic Heisenberg honeycomb model. There is an unclear intermediate region in the ground state phase diagram of the model. The most recognized phases are the quantum spin-liquid (QSL) and the antiferromagnetic Ising ordering. From the viewpoint of the quantum correlations, the QSL phase is expected to be entangled. Motivated by this fact, we have calculated the concurrence, the quantum discord (QD), and the entanglement entropy, by using numerical Lanczos and density matrix renormalization group (DMRG) methods. Our results explicitly show that the intermediate region should be entangled supporting the QSL phase.