Lattice QCD study of static quark and antiquark correlations at finite $T$ via entanglement entropies

Abstract

With the aim of clarification of color correlations among quarks, we investigate the color correlation between a static quark and an antiquark (static $q\bar{q}$) below and above the phase transition temperature $T_c$ through the entanglement entropy(EE). By a quenched lattice QCD calculation on an anisotropic lattice adopting the standard Wilson gauge action in the Coulomb gauge, we compute a reduced density matrix $\rho$ defined in the color space, and the entanglement entropy $S_{\mathrm{EE}}$ constructed from $\rho$. The spatial volume is $L^3=24^3$ and the temporal extents are $N_T=12,13,14,15,16,18,20$ and $24$, with a gauge coupling $\beta =5.75$ and a renormalized anisotropy $\xi =4.0$, which corresponds to temperatures between 180 and 370 MeV. From an analysis of $\rho$ and $S_{\mathrm{EE}}$, the color correlation between $q\bar{q}$ pairs is obtained as a function of the interquark distance $R$ and the temperature $T$. Below $T_c$, the $R$-dependence of the color correlation resembles that at $T=0$: the quark's color correlation gradually decreases as $R$ increases due to the color screening by in-between gluons. Above $T_c$, due to the deconfinement phase transition, the color correlation among quarks is found to quickly dissappear. Further, we investigate the color screening effect via the screening mass defined by $\rho$, and discuss the differences in the screening properties between the small and large R regions.

Comments: 8 pages, 4 figures