Entanglement in a four qubit J1–J2J1–J2 Heisenberg XXZ system with Dzialoshinskii–Moriya interaction

• We consider both the nearest and the next nearest neighboring interactions.
• Dzialoshinskii–Moriya (DM) interaction enhances the nearest neighboring entanglement.
• Frustration augments the entanglement between the next nearest neighboring qubits.
• Contribution of frustration on entanglement is more effective than DM interaction.

In this study, we investigate the entanglement properties of a four qubit anisotropic Heisenberg XXZ system which has the nearest neighboring (NN), the next nearest neighboring (NNN) and Dzialoshinskii–Moriya (DM) interactions. Calculations of the ground state and thermal entanglement are carried out in terms of concurrence for selected ranges of control parameters such as DM interaction, anisotropy and frustration. From the results obtained, we see that DM interaction and the frustration play an active role on the ground state entanglement between NN and NNN qubits, respectively. We also see that frustration parameter αα exhibits positive effects on the thermal entanglement especially between NNN qubits. Consequently, we show that effective control of entanglement can be obtained by employing competing effects of the control parameters in this general Heisenberg model which is constructed by considering not only NN interaction but also NNN and DM interactions.