Role of external fields in enhancing long-distance entanglement at finite temperatures

TL;DR

This paper studies how external fields can enhance the temperature range for entanglement in XYZ-spin chains, revealing limits based on spin separation and conservation laws, with numerical demonstrations.

Contribution

It provides a general theoretical framework for understanding how external fields influence entanglement at finite temperatures in spin chains, including bounds on critical temperature increases.

Findings

External fields can increase the critical temperature for entanglement.

Entanglement vanishes above a finite temperature when end spins are separated by two or more spins.

For one-spin separation, entanglement persists at all temperatures with optimal external fields.

Abstract

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.