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Chinese Physics Letters

Entanglement in Ising Chain with Inhomogeneous Magnetic Field

Cenk Akyüz, Ekrem Aydmer

Published May 1, 2008• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/25/5/010

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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.
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The quantum entanglement of the ground state and the thermal entanglement of the mixed thermal state of a three-qubit system with the Heisenberg interaction are investigated in detail in the presence of an inhomogeneous magnetic field. The concurrence of the model is compared with the magnetization, and the threshold temperature of the entanglement is discussed. The effects of the magnetic field and the coupling coefficient in the thermal entanglement are also examined by considering the concurrence of the three-qubit and two-qubit systems. We found that the thermal entanglement of the system exists at temperatures below the threshold temperature even if the ground state is unentangled.
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.
Ground state entanglement and thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of the different Dzyaloshinski-Moriya interaction and inhomogeneous magnetic field are investigated. By the concept of concurrence, we find that the inhomogeneity of the magnetic field may make entanglement last for a long time and the critical temperature is dependent on J z and b . The entanglement can be increased by increasing the temperature in some cases. We also find that the x -component parameter D x has a higher critical temperature and more entanglement for a certain condition than the z -component parameter D z .
Taking Dzyaloshinskii-Moriya(DM)effect interaction into account,the entanglement of two-qubit Ising model in an inhomogeneous magnetic field is investigated by means of Negativity theory.It is shown that the existence of DM interaction can obviously enhance the entanglement and put it into a maximum while the magnetic field reduces the entanglement.In addition,low temperature also plays a positive role in entanglement.Moreover,the influence of inhomogeneous magnetic field is also investigated. These effects indicate that one can control the thermal entanglement by manipulation of DM interaction, the homogeneous and inhomogeneous magnetic field and temperature.