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arXiv:0705.0386 · New Journal of Physics

Bound entanglement in the XY model

Dario Patanè, Rosario Fazio, Luigi Amico A

Published Sep 11, 2007• 29 citations
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Abstract

We study the multi-spin entanglement for the 1D anisotropic XY model concentrating on the simplest case of three-spin entanglement. As compared to the pairwise entanglement, three-party quantum correlations have a longer range and they are more robust on increasing the temperature. We find regions of the phase diagram of the system where bound entanglement (BE) occurs, both at zero and finite temperature. BE in the ground state can be obtained by tuning the magnetic field. Thermal BE emerges naturally due to the effect of temperature on the free ground state entanglement.

DOI
10.1088/1367-2630/9/9/322

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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.
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.