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Journal of Hubei University

Thermal entanglement in a four-qubit Heisenberg spin chain with the nonuniform external magnetic fields

Wanqiang Cao

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The entanglement properties in the four-qubit Heisenberg XX model in the presence of an external inhomogeneous magnetic field are investigated.The analytical expressions for the measures of entanglement in the system with periodic boundary conditions are obtained.It is found that a high pair entanglement can be obtained.It means that magnetic impurities in the system can enhance thermal entanglement of some qubit pairs.

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 26, 2007•0 citations
The entanglement properties in the four-qubit Heisenberg XX model in the presence of an external inhomogeneous magnetic field are investigated.The analytical expressions for the measures of entanglement in the system with periodic boundary conditions are obtained.It is found that a high pair entanglement can be obtained.It means that magnetic impurities in the system can enhance thermal entanglement of some qubit pairs.
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We study the entanglement in the three-site Heisenberg XY model with nonuniform external magnetic fields and obtain analytic expressions for the measures of entanglement in the system with both the periodic and the open boundary conditions. We show that both the ground state and the excited states of the system possess remarkable entanglement properties and the entanglement clearly depends on the magnitude of external fields. We obtain the pairwise thermal entanglement of the system. We also discuss the boundary effects on the entanglement.
We investigate the thermal entanglement of two-qubit anisotropic Heisenberg XY model in the presence of an external nonuniform magnetic field B along the z-axis. Concurrence, the measure of entanglement is calculated and its property is studied in different cases. Two best models, Ising model under a uniform magnetic and isotropic model in a nonuniform magnetic field, are discovered. In the two models, the critical temperature Tc (above which there is no entanglement) can be enhanced and its concurrence is maximal.
We investigate the thermal entanglement in the two-qubit Heisenberg XY model with a nonuniform magnetic field. Concurrence, the measurement of entanglement, is calculated. The behavior of concurrence is present at three different cases. Contrary to the uniform magnetic field case, we find that the entanglement and the critical temperature TC{T}_{C}TC​ may be enhanced under a nonuniform magnetic field.
In this paper, the entanglement in a spin-1 Heisenberg XXZ chain with uniform and nonuniform external magnetic field is investigated in the terms of the measure of entanglement called 'negativity'. The effects of the external magnetic field, the anisotropy parameter and the temperature on the negativity are discussed respectively. It can be seen that the entanglement in this spin chain for any temperature is symmetric with respect to zero magnetic field. We calculate the partially transposed density matrix and give qualitatively results at different temperatures. In order to show the results clearly, the behavior of negativity is presented for five different cases. It can be found that the temperature and the external magnetic field can effect the feature of the thermal entanglement significantly. In addition, under certain condition, the negativity may be enhanced under a nonuniform magnetic field.