The entanglement of the XY spin chain in a random magnetic field

TL;DR

This paper studies how random magnetic fields and thermal fluctuations influence entanglement in the ferromagnetic XY spin chain, revealing conditions under which entanglement is generated or suppressed.

Contribution

It demonstrates the role of random magnetic fields and temperature in generating and affecting entanglement in the XY model, highlighting the impact of the field's distribution variance.

Findings

Random magnetic fields generate entanglement in the ferromagnetic XY model.

Thermal fluctuations can also induce entanglement.

The behavior of entanglement maxima depends on the variance of the magnetic field distribution.

Abstract

We investigate the entanglement of the ferromagnetic XY model in a random magnetic field at zero temperature and in the uniform magnetic field at finite temperatures. We use the concurrence to quantify the entanglement. We find that, in the ferromagnetic region of the uniform magnetic field $h$, all the concurrences are \textit{generated} by the random magnetic field and by the thermal fluctuation. In one particular region of $h$, the next-nearest neighbor concurrence is generated by the random field but not at finite temperatures. We also find that the qualitative behavior of the maximum point of the entanglement in the random magnetic field depends on whether the variance of its distribution function is finite or not.