Global entanglement in XXZ chains

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.