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

We study the color correlation between static quark and antiquark ($q\bar q$) in the confined phase via reduced density matrices $\rho$ 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 $L^3 = 8^3$, $16^3$, $32^3$ and $48^3$, with the gauge couplings $\beta = 5.7$, 5.8 and 6.0. Each element of the reduced density matrix in the sub space of quarks' color degrees of freedom of the $q\bar q$ pair is calculated from staples defined by link variables. As a result, we find that $\rho$ is well written by a linear combination of the strongly correlated $q\bar q$ pair state with the color-singlet component and the uncorrelated $q\bar q$ pair state with random color configurations. We compute the Renyi entropies $S^{\rm Renyi}$ from $\rho$ to investigate the $q\bar q$ distance dependence of the color correlation of the $q\bar q$ pair and find that the color correlation is quenched as the distance increases.