Separability conditions and limit temperatures for entanglement detection in two qubit Heisenberg XYZ models

We examine the entanglement of general mixed states of a two qubit Heisenberg XYZ chain in the presence of a magnetic field, and its detection by means of different criteria. Both the exact separability conditions and the weaker conditions implied by the disorder and the von Neumann entropic criteria are analyzed. The ensuing limit temperatures for entanglement in thermal states of different XYZ models are then examined and compared with the limit temperature of the symmetry-breaking solution in a mean field type approximation. The latter, though generally lower, can also be higher than the exact limit temperature for entanglement in certain cases, indicating that symmetry-breaking does not necessarily entail entanglement. The reentry of entanglement for increasing temperatures is also discussed.