We study the color correlation between the static quark and antiquark (
qq) in the confined phase via reduced density matrices $\ensuremath{\rho}$ 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
L3=83,
163,
323, and
483, with the gauge couplings $\ensuremath{\beta}=5.7$, 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 $\ensuremath{\rho}$ 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 $\ensuremath{\rho}$ 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.
With the aim of clarification of color correlations among quarks, we investigate the color correlation between a static quark and an antiquark (static
qq) below and above the phase transition temperature
Tc 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 $\ensuremath{\rho}$ defined in the color space and the entanglement entropy
SEE constructed from $\ensuremath{\rho}$. The spatial volume is
L3=243, and the temporal extents are
NT=12, 13, 14, 15, 16, 18, 20 and 24, with a gauge coupling $\ensuremath{\beta}=5.75$ and a renormalized anisotropy $\ensuremath{\xi}=4.0$, which corresponds to temperatures between 180 and 370 MeV. From an analysis of $\ensuremath{\rho}$ and
SEE, the color correlation between
qq pairs is obtained as a function of the interquark distance
R and the temperature
T. Below
Tc, 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
Tc, due to the deconfinement phase transition, the color correlation among quarks is found to quickly disappear. Further, we investigate the color screening effect via the screening mass defined by $\ensuremath{\rho}$ and discuss the differences in the screening properties between the small and large R regions.
In recent work Amorosso et al. (2024), we computed a novel flux tube entanglement entropy (FTE) of the color flux tube stretched between a heavy quark-antiquark pair on a Euclidean lattice in (2+1)D Yang–Mills theory. Our numerical results suggested that FTE can be partitioned into an internal color entanglement entropy and a vibrational entropy corresponding to the transverse excitations of a QCD string, with the latter described by a thin string model. Since the color flux tube does not have transverse excitations in (1+1)D Yang–Mills theory, we use this simpler framework to perform an exact analytical computation of the contribution of the internal color degrees of freedom to FTE. For the multipartite partitioning of the color flux tube, we find the remarkable result that FTE depends only on the dimension of the color group representation and the number of times the flux tube crosses the boundary between the traced and untraced spatial regions but not on the string length. Our proof is independent of whether the replica and region boundaries on the lattice are placed on vertices or in plaquette centers.
Recent lattice QCD studies have revealed an excess entanglement entropy (flux tube entanglement entropy, FTE 2 ) in the color flux tube between static quark–antiquark pairs, which grows linearly with the quark separation. In this paper, we illustrate a possible analogy in a simplified string-net model based on the Fibonacci fusion category, where the non-trivial object [Formula: see text] (analogous to color charge) cannot exist in isolation due to the fusion rule [Formula: see text], naturally exhibiting “confinement”. We compute the entanglement entropy of the flux tube connecting two [Formula: see text] objects and find an entropy density of [Formula: see text] ([Formula: see text] is the golden ratio), which quantitatively agrees with the lattice QCD measured FTE 2 density (approximately 0.3–0.5). Minimizing the free energy [Formula: see text] at fixed temperature and volume, the competition between the energy term [Formula: see text] and the entropy term [Formula: see text] yields a confinement-deconfinement phase transition at critical temperature [Formula: see text]. This model provides a heuristic demonstration platform as a minimal model for understanding the entropic properties of the QCD flux tube.
In local quantum field theory, the entanglement entropy of a region is divergent due to the arbitrary short-wavelength correlations near the boundary of the region. Quantum gravitational fluctuations are expected to cut off the entropy of the ultraviolet modes. Guided by this, we study the entanglement entropy in closed string theory. We factorize the configuration space of closed strings based on the position of the center of mass. We then compute the one-loop Rényi partition functions corresponding to this factorization using the replica method and string field theory. The short-wavelength modes are cut off at the string scale and the one-loop entanglement entropy is ultraviolet-finite. A non-trivial path integration measure, required to produce the correct one-loop vacuum amplitude, plays a key role.
We construct a toy model of a nucleon, in which three static quarks interact via a SU(3) gauge field on a planar honeycomb lattice. The dynamics of the gauge field is described by the Kogut-Susskind Hamiltonian, truncated to the lowest three SU(3) irreducible representations. We show that the internal structure of the toy nucleon reflects salient features of the physical nucleon state. We then find the entanglement entropy of the gauge field within the nucleon state and compute its time evolution after a quench, in which all three valence quarks are suddenly removed. We show that the entanglement entropy in the final state is dominated by the dynamically generated contribution rather than the initial state entropy.