  We investigate the end-to-end entanglement of a general XYZ-spin chain at the
non-zero temperatures. The entanglement usually vanishes at a certain critical
temperature $T_c$, but external fields can make $T_c$ higher. We obtain a
general statement on the increase of the critical temperature $T_c$ by the
external fields. We prove that if the two end spins are separated by two spins
or more, the critical temperature cannot be higher than a certain finite
temperature $bar{T}_c$ ($T_c le bar{T}_c$), that is, the entanglement must
vanish above the temperature $bar{T}_c$ for any values of the external fields.
On the other hand, if the two end spins are separated by one spin, the
entanglement maximized by the external fields exhibits a power law decay of the
temperature, being finite at any temperatures. In order to demonstrate the
former case, we numerically calculate the temperature $bar{T}_c$ in $XX$ and XY
four-spin chains. We find that the temperature $bar{T}_c$ shows qualitatively
different behavior, depending on the conservation of the angular momentum in
the $z$ direction.

Quantum Physics