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Chinese Physics B

Quantum steering in Heisenberg models with Dzyaloshinskii–Moriya interactions

Huizhen Li, Rong-Sheng Han, Ye-Qi Zhang, Liang Chen

Published Dec 1, 2018• 5 citations
Publisher

Abstract

In this work, we study the quantum steering in two-qubit Heisenberg models with Dzyaloshinskii–Moriya (DM) interaction and an external magnetic field. We find that the steerable weight (SW) and the critical temperature where SW → 0 can be enhanced by the DM interactions. In the special case where the magnetic field is vanishing and the two spins are ferromagnetically coupled, the DM interaction can tune the zero-temperature SW from zero to a finite value. In addition to the SW, some other measurements used to identify the quantum entanglement and quantum correlations are investigated, i.e. , the concurrence, the quantum discord, and the robustness of coherence. In the strong magnetic field limit, our results show that the SW is dramatically different from the other measurements.

DOI
10.1088/1674-1056/27/12/120304

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In this work, we study the quantum steering in two-qubit Heisenberg models with Dzyaloshinskii–Moriya (DM) interaction and an external magnetic field. We find that the steerable weight (SW) and the critical temperature where SW → 0 can be enhanced by the DM interactions. In the special case where the magnetic field is vanishing and the two spins are ferromagnetically coupled, the DM interaction can tune the zero-temperature SW from zero to a finite value. In addition to the SW, some other measurements used to identify the quantum entanglement and quantum correlations are investigated, i.e. , the concurrence, the quantum discord, and the robustness of coherence. In the strong magnetic field limit, our results show that the SW is dramatically different from the other measurements.
We investigate the behavior of quantum steering for a pair of quantum qubits described by the Heisenberg model with external magnetic field and in equilibrium with a reservoir at temperature T . Generally, the steerable weight, which is used to identify the steerability, is suppressed by thermal fluctuations. When the magnetic field is vanishing, the steerable weight behaves like the quantum entanglement. When the magnetic field is not zero, the steerable weight is dramatically different from the other quantities used to identify the quantum correlations between the two spins, i.e. , the concurrence, quantum discord and coherence. In the strong magnetic field limit, all of the other quantities we studied are vanishing for the Ising model, while steerable weight tends to one. This demonstrates that the strong transverse magnetic field is helpful to preserve the quantum steerability of the Ising model.
We investigate the pairwise thermal quantum discord in a three-qubit XXZ model with Dzyaloshinskii—Moriya (DM) interaction. We find that the effects of DM interaction on antiferromagnetic system is distinct from that of ferromagnetic system. The magnetic field supplemented with DM term contribute to enhance the range of quantum discord. It is revealed that the situations where quantum discord fails to indicate a sudden change of groundstate at finite temperature though indicating such a sudden change of groundstate at zero temperature. Dynamics of pairwise thermal quantum discord is considered as well. Thermal quantum discord vanishes in asymptotic limit regardless of its initial values, however, thermal entanglement suddenly disappears in finite time.
We have investigated the quantum discord (QD) of the thermal density matrix of spin-1/2 Heisenberg chains with Dzyaloshinskii–Moriya (DM) interaction. With fermionization technique, we study the mutual effect of DM interaction and the external magnetic field on the QD and the entanglement. Our analysis implies that the DM interaction can enhance the QD while the external magnetic field will shrink the QD. By a comparison between the entanglement and the QD, we find that the QD is more robust to the temperature and to the external magnetic field than the entanglement of formation (EoF) in the sense that the EoF takes a zero value while the QD does not for high temperature and strong external magnetic field. This point confirms the conclusion that there exist some separable states containing non-zero QD.
In this paper, we study the improvement and manipulation of pairwise thermal entanglement in one-dimentional three-qubit Heisenberg model, where Dzyaloshinskii-Moriya (DM) interaction is considered and concurrence is calculated to research this entanglements property. The results show that for XXX model, DM interaction can induce entanglement in the antiferromagnetic and ferromagnetic spin chains although the required critical values are different for these cases. For XXZ model, by introducing DM interaction D, antiferromagnetic spin chain has entanglement which is absent when D=0, and in addition, for antiferromagnetic and ferromagnetic cases, DM interaction D and the anisotropy parameter Δ have different effects on entanglement. As a result, the entanglement can be controlled and enhanced by choosing appropriate DM interaction and anisotropy parameter. Furthermore, we find that at the same temperature, no matter for antiferromagnetic or ferromagnetic spin chains, the critical DM interaction inducing entanglement should be greater in a three-qubit XXZ model than that in a two-qubit XXZ model.
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.
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.