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Journal of Hengyang Normal University

Violation of the Bell Inequality in the Heisenberg Model with Dzyaloshinski-Moriya Interaction

Xiaoling Yin

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

We investigate the violation of the Bell inequality for thermal states of qubits in the two-qubit and three-qubit Heisenberg models with Dzyaloshinski-Moriya(DM) interaction.The results indicate that the Bell inequality can be violated in the case of two-qubit Heisenberg model but not violated in the case of three-qubit Heisenberg model at any DM interaction and temperature.

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We investigate the violation of the Bell inequality for thermal states of qubits in the two-qubit and three-qubit Heisenberg models with Dzyaloshinski-Moriya(DM) interaction.The results indicate that the Bell inequality can be violated in the case of two-qubit Heisenberg model but not violated in the case of three-qubit Heisenberg model at any DM interaction and temperature.
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.
This paper investigates the thermal pairwise entanglement of a three-qubit Heisenberg XXZ chain in the presence of the Dzyaloshinski–Moriya (DM) anisotropic antisymmetric interaction and quantum teleportation when using the Heisenberg chain as a channel. The entanglement dependences on the DM interaction and temperature are given in detail. It obtains the relation between the concurrence and average fidelity, and shows that the same concurrence can lead different average fidelities. Moreover, it finds the thermally entangled states which do not violate the Bell inequalities, and can still be used for quantum teleportation.