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arXiv:2407.08463

Investigating the evolution of quantum entanglement of a qubit-qubit system with Dzyaloshinskii-Moriya interaction in the presence of magnetic fields

Seyed Mohsen Moosavi Khansari, Fazlollah Kazemi Hasanvand

Published Jul 11, 2024• 0 citations
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Abstract

In this paper, the quantum entanglement dynamics of a qubit qubit compound system in the isotropic XXX Heisenberg and anisotropic XYZ models with DM interaction under magnetic fields is investigated. The system's initial state is considered as a spin coherence state, and the entanglement dynamics of this compound system is analyzed using the negativity criterion as an entanglement measure to assess the impact of DM interaction and magnetic fields.

DOI
10.48550/arxiv.2407.08463

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In this paper, the quantum entanglement dynamics of a qubit qubit compound system in the isotropic XXX Heisenberg and anisotropic XYZ models with DM interaction under magnetic fields is investigated. The system's initial state is considered as a spin coherence state, and the entanglement dynamics of this compound system is analyzed using the negativity criterion as an entanglement measure to assess the impact of DM interaction and magnetic fields.
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The thermal entanglement in a two-qubit anisotropic Heisenberg XXZ system, also XYZ system, with Dzyaloshinskii-Moriya (DM) couplings in an inhomogenous magnetic field, was studied. The effects of these two kinds of anisotropies on the thermal entanglement have been studied in detail in the concept for concurrence, the measure of entanglement. The analytical expressions of concurrence are obtained for this model. It is found that the DM interaction can enhance thermal entanglement and can be efficiently controlled by the DM interaction parameter and ehchange interaction Jx, Jy and Jz. When D is large enough, the entanglement can exist for larger temperatures and strong magnetic field. We also analysed thermodynamic properties of Heisenberg model and the most important results were shown in the paper.
We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.
Abstract In this study, we investigate the entanglement dynamics of two qutrits under Dzyloshinsky–Moriya (DM) interaction within a spin-qubit environment, influenced by two identical time-dependent external magnetic fields described by B ( 1 − e − γ t ) . To quantify the entanglement between the two spin qutrits, we employ the Holstein–Primakoff transformation to compute the negativity measure. Our analysis reveals that the entanglement dynamics are affected by various factors, including the initial states of the spin environment and the qutrits, the system-environment coupling strength, the strength of the DM interaction, and the intensity of the external magnetic field. Notably, we find that increasing the spin coherence amplitude and the intensity of the magnetic field contributes to the stabilization of entanglement. In the weak coupling regime, an increase in the DM interaction enhances entanglement, irrespective of whether a magnetic field is present. Conversely, in the strong coupling regime, an increase in the DM interaction negatively impacts entanglement, regardless of the presence or absence of a magnetic field.
This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii–Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states cos θ |00⟩ + sin θ |11⟩ and cos φ |01⟩ + sin φ |10⟩ at zero temperature. The influences of Dzyaloshinskii–Moriya interaction D , anisotropic parameter Δ and environment coupling strength γ on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii–Moriya interaction D acts on the time evolution of entanglement only when the initial state is cos φ |01⟩ + sin φ |10⟩. Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii–Moriya interaction D , depends on the anisotropic parameter Δ and the environment coupling strength γ.