Lattice QCD study of static quark and antiquark correlations via entanglement entropies

We study the color correlation between the static quark and antiquark (qq¯) in the confined phase via reduced density matrices ρ defined in color space. We adopt the standard Wilson gauge action and perform quenched calculations with the Coulomb gauge condition for reduced density matrices. The spatial volumes are L3=83, 163, 323, and 483, with the gauge couplings β=5.7, 5.8, and 6.0. Each element of the reduced density matrix in the subspace of quarks' color degrees of freedom of the qq¯ pair is calculated from staples defined by link variables. As a result, we find that ρ is well written by a linear combination of the strongly correlated qq¯ pair state with the color-singlet component and the uncorrelated qq¯ pair state with random color configurations. We compute the Renyi entropies SRenyi from ρ to investigate the qq¯ distance dependence of the color correlation of the qq¯ pair and find that the color correlation is quenched as the distance increases.