Quantum entanglement in SU(3) lattice Yang-Mills theory at zero and finite temperatures

TL;DR

This study investigates the entanglement entropy in SU(3) lattice Yang-Mills theory at different temperatures, revealing distinct behaviors in confinement and deconfinement phases through lattice simulations.

Contribution

It provides the first lattice calculation of $ ext{alpha}$ entanglement entropy in SU(3) Yang-Mills theory at finite temperatures, highlighting phase-dependent entanglement properties.

Findings

In confinement phase, the derivative of $ ext{alpha}$ entropy scales as 1/l^3.

In deconfinement phase, the $ ext{alpha}$ entropy saturates at large l.

Saturation value matches the thermal entropy, indicating volume law behavior.

Abstract

We examine the entanglement properties of the Yang-Mills theory by calculating $\alpha$ entanglement entropy with $\alpha=2$ using a SU(3) quenched lattice gauge simulation both in the confinement and the deconfinement phases. In the confinement phase, the derivative of the $\alpha$ entropy with respect to the size $l$ of the subregion, whose entanglement properties are interested in, scales as $1/l^3$, and a clear discontinuity cannot be found within our statistical errors. The $\alpha$ entropy in the deconfinement phase saturates at large $l$. The saturation value is comparable with the thermal entropy of the pure Yang-Mills theory, indicating that the $\alpha$ entropy obeys the volume law at large $l$ in the deconfinement phase.