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

Abstract

We examine the entanglement properties of the Yang-Mills theory by calculating $α$ entanglement entropy with $α=2$ using a SU(3) quenched lattice gauge simulation both in the confinement and the deconfinement phases. In the confinement phase, the derivative of the $α$ 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 $α$ 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 $α$ entropy obeys the volume law at large $l$ in the deconfinement phase.