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/l3, 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.