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Low Temperature Physics

Macroscopic thermal entanglement in a spin chain caused by the magnetic field: Inhomogeneity effect

Andrei A. Zvyagin

Published Mar 1, 2012• 4 citations
Publisher

Abstract

The influence of the inhomogeneity on the macroscopic thermal pairwise entanglement for the system of coupled spins 1/2 (qubits) has been studied. The most important effect of the inhomogeneity on the thermal entanglement is in the new role of the external potential (magnetic field), which can produce nonzero entanglement for qubits, situated not far from the inhomogeneity.

DOI
10.1063/1.3691529

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The influence of the inhomogeneity on the macroscopic thermal pairwise entanglement for the system of coupled spins 1/2 (qubits) has been studied. The most important effect of the inhomogeneity on the thermal entanglement is in the new role of the external potential (magnetic field), which can produce nonzero entanglement for qubits, situated not far from the inhomogeneity.
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We have numerically calculated the thermal entanglement of a two-qubit system at low temperatures in a isotropic Ising chain under an inhomogeneous magnetic field. It is shown that in the homogeneous magnetic field, the two-qubit system has entangled states. It is concluded that the presence of the inhomogeneity in the magnetic field plays an effective role on the entangled states. Finally, it is suggested that the inhomogeneity in the magnetic field can be used to create two separated entangled formations in a two-qubit system.
We study the entanglement of thermal and ground states in the Heisenberg XY spin chain with an inhomogeneous magnetic field.A general result is found that for two-qubit case,pairwise entanglement is independent of the sign of coupling constant J,magnetic field B,anisotropic parameter γ and inhomogeneous parameter b of the magnetic field.At zero absolute temperature,an analytical expression of concurrence C is given through which we show that the critical magnetic field Bc increases with the increase of inhomogeneity.At finite temperature,we show analytically for the isotropic case and numerically for the anisotropic case that the thermal entanglement can be apparently enhanced by introducing the inhomogeneity of the magnetic field.We also show that for isotropic case the critical temperature Tc is alone an increasing function of the inhomogeneous parameter b,while for anisotropic case,it is determined by both B and b.
The thermal entanglement in a two-qubit Heisenberg XXZXXZXXZ spin chain is investigated under an inhomogeneous magnetic field bbb. We show that the ground-state entanglement is independent of the interaction of zzz-component Jz{J}_{z}Jz​. The thermal entanglement at the fixed temperature can be enhanced when Jz{J}_{z}Jz​ increases. We strictly show that for any temperature TTT and Jz{J}_{z}Jz​, the entanglement is symmetric with respect to zero inhomogeneous magnetic field, and the critical inhomogeneous magnetic field bc{b}_{c}bc​ is independent of Jz{J}_{z}Jz​. The critical magnetic field Bc{B}_{c}Bc​ increases with the increasing $\ensuremath{\mid}b\ensuremath{\mid}$ but the maximum entanglement value that the system can arrive at becomes smaller.
The effects of spin-spin interaction on thermal entanglement of a two-qubit Heisenberg XYZ model with different inhomogeneous magnetic fields are investigated. It is shown that the entanglement is dependent on the spin-spin interaction and the inhomogeneous magnetic fields. The larger the J i (i-axis spin-spin interaction), the higher critical value the B i (i-axis uniform magnetic field) has. Moreover, in the weak-field regime, the larger J i corresponds to more entanglement, while in the strong-field regime, different J i correspond to the same entanglement. In addition, it is found that with the increase of J i , the concurrence can approach the maximum value more rapidly for the smaller B i , and can reach a larger value for the smaller b i (i-axis nonuniform magnetic field). So we can get more entanglement by increasing the spin-spin interaction J i , or by decreasing the uniform magnetic field B i and the nonuniform magnetic field b i .