Entanglement and quantum correlations in the honeycomb graphene lattice within the Hubbard model

In this paper, we study the quantum correlations, particularly entanglement, between two qubits in graphene lattices. This study considers the short-range electron-electron Coulomb interactions as introduced by the Hubbard model and examines entanglement and other quantum correlations using the logarithmic negativity EN and the measurement-induced disturbance (MID) quantifiers, respectively. The results show that the on-site repulsion U, the nearest-neighbor interaction V between two qubits can promote entanglement up to a certain limit of U and V, but beyond entanglement, they can destroy other quantum correlations. These parameters can be seen as potentials generated near the two qubits, and they have a significant impact role in determining the amount and nature of quantum correlations in the system. Additionally, we have noted that the temperature T and the hopping parameter t also affect the quantum correlations in the system. Moreover, we found that MID is more robust than EN. That is means that even when there is no entanglement present, quantum correlations are still present in the interacting two-qubit states, which can be detected by MID quantifier.