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Modern Physics Letters A

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

Nabil Habiballah, Ahmed Salah, L. Jebli, Mohamed Amazioug, Jamal El Qars, Mostafa Nassik

Published Apr 8, 2020• 15 citations

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.

DOI: 10.1142/s0217732320501382

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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.

We investigate the thermal entanglement in a spin-1/2 Ising–Heisenberg diamond chain, in which the vertical Heisenberg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii–Moriya (DM) interaction contributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including D z and D x , on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interaction, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters ( D z and D x ) have remarkably different influences on the entanglement. Different from the case D z , there is the non-monotonic variation of the concurrence with temperature in the case D x , and additionally the DM interaction D x can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case D x is larger than that of the case D z .

In this paper, we investigate the pairwise quantum correlations in a two-qubit anisotropic Heisenberg model under the interplay of Calogero–Moser (CM) and Dzyaloshinsky–Moriya (DM) interactions in the presence of the homogeneous and inhomogeneous magnetic fields. We employ, respectively, the logarithmic negativity and local quantum uncertainty (LQU) to characterize the degree of entanglement and the amount of quantum correlations between the two parties of the considered system in equilibrium with a thermal reservoir. We analyze and compare the behaviors of the two quantum correlation quantifiers in the thermal state of the chain spin system and we discuss how relative distance between spins, equilibrium temperature, DM interaction coupling parameter and the external magnetic fields strengths influence the variations of both quantum correlation measures in such system.

The quantum entanglement between two spins in the Ising model with an added Dzyaloshinsky–Moriya (DM) interaction and in the presence of the transverse magnetic field is studied. The exchange interaction is considered as a function of the distance between spins. The negativity as a function of magnetic field, exchange and DM interaction is calculated. The effect of the distance between spins is studied based on the negativity. In addition, the effect of the thermal fluctuation on the negativity is also investigated.

Thermal entanglement of a two-qubit Ising chain subjected to an external magnetic field and Dzyaloshinsky—Moriya (DM) interaction is examined. The effect of magnetic field, strength of DM interaction and temperature are analyzed by adopting negativity of partial transpose as the measure of entanglement. It is shown that when the DM interaction along the Ising axis is considerable, thermal entanglement can be sustained for a higher temperature. The usefulness of longitudinal DM interaction over the one that is perpendicular to the Ising axis, in the manipulation and control of entanglement at a feasible temperature, is illustrated.