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 $S_{\rm EE}$ 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 $S_{\rm EE}$, 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.
Highlights
Color confinement is one of the important nonperturbative features of quantum chromodynamics (QCD), which is the fundamental theory of the strong interaction
By means of an entanglement entropy (EE) defined by reduced density matrices ρ in a color space, we have investigated the color correlation of static qqsystems at finite temperatures
As the temperature increases, such qqcorrelation is quickly lost during the phase transition at T 1⁄4 Tc leading to an acute increase of the EE, which reflects the drastic modification of the gluon configuration at the phase transition
Summary
Color confinement is one of the important nonperturbative features of quantum chromodynamics (QCD), which is the fundamental theory of the strong interaction. Above the phase transition temperature Tc, the confining potential among quarks vanishes, and colored states are allowed, which has been confirmed in lattice QCD calculations [5,6]. [8], we computed the color correlation between a static quark and antiquark (qq ) pair by means of an entanglement entropy (EE) defined by the reduced density matrix ρ in the color space at zero temperature. Through the analysis of S and ρ [8], we investigate the dependence of the color correlation on the interquark distance R and the temperature T below and above Tc. In Sec. II, we present the formalism necessary to compute the reduced density matrix ρ of the qqsystem and its EE S.
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