We examine the thermal entanglement of $XXZ$-type Heisenberg chains in the presence of a uniform magnetic field along the $z$ axes through the evaluation of the negativity associated with bipartitions of the whole system and subsystems. Limit temperatures for nonzero global negativities are shown to depend on the asymmetry $\Delta$, but not on the uniform field, and can be much higher than those limiting pairwise entanglement. It is also shown that global bipartite entanglement may exist for $T>0$ even for $\Delta ⩾1$, i.e., when the system is fully aligned (and hence separable) at $T=0$, and that the bipartition leading to the highest limit temperature depends on $\Delta$.

• Received 17 October 2005

DOI:https://doi.org/10.1103/PhysRevA.73.022347