Quantum entanglement and violation of Bell’s inequality in dipolar interaction system under Dzyaloshinsky–Moriya interaction

Abstract

The Dzyaloshinsky–Moriya (DM) interaction contributes to some unusual and interesting magnetic properties in real materials, thus playing an important role in the degree of quantum entanglement in Heisenberg quantum spin models. In [C. S. Castro, O. S. Duarte, D. P. Pires, D. O. Soares-Pinto and M. S. Reis, Phys. Lett. A 380, 1571 (2016)], it has been investigated about the non-locality and the thermal entanglement in a dipolar spin thermal system without DM interaction. In this work, we study the entanglement in the thermal state of inhomogeneous Heisenberg coupling under the presence of the DM interaction along the [Formula: see text]-axis. More precisely, we analyze the effect of the DM interaction on non-locality phenomena and quantum entanglement as measured by negativity and Von Neumann entropy. We show that by comparing with [C. S. Castro, O. S. Duarte, D. P. Pires, D. O. Soares-Pinto and M. S. Reis, Phys. Lett. A 380, 1571 (2016)], the local quantum states become more pronounced, when the DM interaction is taken into account. This fact is well confirmed by noting that Von Neumann entropy is destroyed in the presence of the DM interaction. It can be deduced that the Dzyaloshinsky–Moriya (DM) interaction makes the thermal states less correlated.