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arXiv:quant-ph/0509009 · Physical Review A

Thermal entanglement in a two-qubit Heisenberg XXZ spin chain under an inhomogeneous magnetic field

Guo‐Feng Zhang, Shu‐Shen Li

Published Sep 2, 2005• 227 citations
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Abstract

The thermal entanglement in a two-qubit Heisenberg $XXZ$ spin chain is investigated under an inhomogeneous magnetic field $b$. We show that the ground-state entanglement is independent of the interaction of $z$-component ${J}_{z}$. The thermal entanglement at the fixed temperature can be enhanced when ${J}_{z}$ increases. We strictly show that for any temperature $T$ and ${J}_{z}$, the entanglement is symmetric with respect to zero inhomogeneous magnetic field, and the critical inhomogeneous magnetic field ${b}_{c}$ is independent of ${J}_{z}$. The critical magnetic field ${B}_{c}$ increases with the increasing $\ensuremath{\mid}b\ensuremath{\mid}$ but the maximum entanglement value that the system can arrive at becomes smaller.

DOI
10.1103/physreva.72.034302

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The thermal entanglement in the Heisenberg XYZ\mathrm{XYZ}XYZ chain is investigated in the presence of an external magnetic field B. In the two-qubit system, the critical magnetic field Bc{B}_{c}Bc​ is increased by introducing the interaction of the z component of two neighboring spins Jz.{J}_{z}.Jz​. This interaction not only improves the critical temperature Tc,{T}_{c},Tc​, but also enhances the entanglement for a particular fixed B. We also analyze the pairwise entanglement between nearest neighbors in three qubits. The pairwise entanglement, for a fixed T, can become strong by controlling B and Jz.{J}_{z}.Jz​.
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