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 non-zero global negativities are shown to depend on the asymmetry $\mathrm{\Delta }$ 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 $\mathrm{\Delta }\ge 1$, 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 $\mathrm{\Delta }$.