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Chinese Physics Letters

Effects of Inhomogeneous Spin Coupling and Anisotropy on Thermal Entanglement

Jin‐Liang Guo, Huang Xiao-Li, He‐Shan Song

Published Jun 1, 2007• 1 citation
Publisher

Abstract

We study the thermal entanglement properties of a simple system that includes three spins inhomogeneously coupled between them with additional anisotropy in their couplings. The main result is the systematic analysis of the concurrence evolution as functions of inhomogeneity, anisotropy and temperature. By adjusting proportional factor of the interaction J and anisotropy parameter Δ, the comparison between concurrences C 12 and C 13 is also presented.

DOI
10.1088/0256-307x/24/6/006

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We study the thermal entanglement properties of a simple system that includes three spins inhomogeneously coupled between them with additional anisotropy in their couplings. The main result is the systematic analysis of the concurrence evolution as functions of inhomogeneity, anisotropy and temperature. By adjusting proportional factor of the interaction J and anisotropy parameter Δ, the comparison between concurrences C 12 and C 13 is also presented.
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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 entanglement properties of a three-spin XXZ Heisenberg chain with three-spin interaction are studied by means of concurrence of pairwise entanglement. We show that ground-state pairwise entanglement, pairwise thermal entanglement, or quantum phase transition is not present in antiferromagnetic spin chain. For the ferromagnetic case, quantum phase transition takes place at Δ = 1 for anisotropic interaction and at some values of three-spin coupling strength, and pairwise thermal entanglement increases when the value of J / T increases and with anisotropic interaction and three-spin interaction decrease. In addition, we find that increasing the anisotropic interaction and the three-spin interaction will decrease critical temperature.
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.