Global entanglement in XXZ chains

TL;DR

This paper investigates how thermal entanglement in XXZ Heisenberg chains depends on temperature, anisotropy, and magnetic field, revealing conditions for global entanglement persistence at finite temperatures.

Contribution

It provides a detailed analysis of the thermal entanglement properties of XXZ chains, highlighting the dependence of entanglement limits on anisotropy and showing global entanglement can exist at higher temperatures than pairwise.

Findings

Global entanglement persists at higher temperatures than pairwise entanglement.

Limit temperatures depend on anisotropy parameter $\Delta$ but not on magnetic field.

Global bipartite entanglement can exist even when the system is fully aligned at zero temperature.

Abstract

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 $\Delta$ 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 $\Delta\geq 1$, 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 $\Delta$.