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arXiv:quant-ph/0407073 · Physical Review A

Thermal entanglement of spins in an inhomogeneous magnetic field

M. Asoudeh, Vahid Karimipour

Published Feb 14, 2005• 135 citations
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Abstract

We study the effect of inhomogeneities in the magnetic field on the thermal entanglement of a two-spin system. We show that in the ferromagnetic case a very small inhomogeneity is capable of producing large values of thermal entanglement. This shows that the absence of entanglement in the ferromagnetic Heisenberg system is highly unstable against inhomogeneity of magnetic fields, which is inevitably present in any solid state realization of qubits.

DOI
10.1103/physreva.71.022308

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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.