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arXiv:2011.10950 · Physical review. D/Physical review. D.

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

TORU T. TAKAHASHI, Yoshiko Kanada-En’yo

Published Feb 11, 2021• 3 citations
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Abstract

With the aim of clarification of color correlations among quarks, we investigate the color correlation between a static quark and an antiquark (static $q\overline{q}$) 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 $\ensuremath{\rho}$ defined in the color space and the entanglement entropy ${S}_{\mathrm{EE}}$ constructed from $\ensuremath{\rho}$. The spatial volume is ${L}^{3}=2{4}^{3}$, and the temporal extents are ${N}_{T}=12$, 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 ${S}_{\mathrm{EE}}$, the color correlation between $q\overline{q}$ 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 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.

DOI
10.1103/physrevd.103.034504

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With the aim of clarification of color correlations among quarks, we investigate the color correlation between a static quark and an antiquark (static qq‾q\overline{q}qq​) below and above the phase transition temperature Tc{T}_{c}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 \ensuremathρ\ensuremath{\rho}\ensuremathρ defined in the color space and the entanglement entropy SEE{S}_{\mathrm{EE}}SEE​ constructed from \ensuremathρ\ensuremath{\rho}\ensuremathρ. The spatial volume is L3=243{L}^{3}=2{4}^{3}L3=243, and the temporal extents are NT=12{N}_{T}=12NT​=12, 13, 14, 15, 16, 18, 20 and 24, with a gauge coupling \ensuremathβ=5.75\ensuremath{\beta}=5.75\ensuremathβ=5.75 and a renormalized anisotropy \ensuremathξ=4.0\ensuremath{\xi}=4.0\ensuremathξ=4.0, which corresponds to temperatures between 180 and 370 MeV. From an analysis of \ensuremathρ\ensuremath{\rho}\ensuremathρ and SEE{S}_{\mathrm{EE}}SEE​, the color correlation between qq‾q\overline{q}qq​ pairs is obtained as a function of the interquark distance RRR and the temperature TTT. Below Tc{T}_{c}Tc​, the RRR-dependence of the color correlation resembles that at T=0T=0T=0: the quark's color correlation gradually decreases as RRR increases due to the color screening by in-between gluons. Above Tc{T}_{c}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 \ensuremathρ\ensuremath{\rho}\ensuremathρ and discuss the differences in the screening properties between the small and large R regions.
We study the color correlation between the static quark and antiquark (qq‾q\overline{q}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{L}^{3}={8}^{3}L3=83, 1631{6}^{3}163, 3233{2}^{3}323, and 4834{8}^{3}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‾q\overline{q}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‾q\overline{q}qq​ pair state with the color-singlet component and the uncorrelated qq‾q\overline{q}qq​ pair state with random color configurations. We compute the Renyi entropies SRenyi{S}^{\text{Renyi}}SRenyi from $\ensuremath{\rho}$ to investigate the qq‾q\overline{q}qq​ distance dependence of the color correlation of the qq‾q\overline{q}qq​ pair and find that the color correlation is quenched as the distance increases.
We study the entanglement of gluon fields in presence of a static QQˉQ\bar QQQˉ​ pair in quenched QCD. Using the replica method, we investigate the q=2q=2q=2 Renyi entropy of the entanglement of gluon fields inside and in the vicinity of the confining QCD string between the quark and the antiquark. We find that there is excess entropy of gluon entanglement compared to vacuum fluctuations. This excess of entanglement entropy is associated with the gluon flux tube, and we find that it has a finite non-zero value in the continuum. We investigate the dependence of gluon entanglement on the geometry of longitudinal and transverse partitioning of the flux tube. Our preliminary results suggest scaling of the entanglement entropy with the area of the boundary overlapping with the flux tube.
We investigate quark-antiquark entanglement in heavy quarkonium within a nonperturbative light-front Hamiltonian framework. By tracing over the antiquark degrees of freedom in the hadronic state vector, we construct the reduced density matrix of the quark subsystem and compute the associated von Neumann entropy. For spin-0 quarkonia, we show that this entropy reduces to the Shannon entropy of the unpolarized transverse momentum dependent parton distribution (TMD), up to constant color and spin contributions. For spin-1 quarkonia, we derive the explicit polarization dependence of the entropy and connect it to polarized and tensor-polarized TMDs. Using light-front wave functions obtained via basis light-front quantization (BLFQ), we evaluate the entanglement entropy for charmonium and bottomonium states, revealing a pronounced sensitivity to the polarization of vector mesons. Furthermore, we resolve the infrared parameter by matching the momentum-space entropy to a harmonic-oscillator representation. Ultimately, these results establish entanglement entropy as a novel probe of nonperturbative quarkonium structure, forging a direct link between quantum information measures and partonic observables.
We study entanglement entropy for 2-dimensional lattice gauge theories with matter fields.For gauge theories, even in lattice space we fail to define entanglement entropy as usual way due to non-local excitations characteristic of theories with constraints.To solve this problem, we apply extended Hilbert space formalism and define entanglement entropy in the generalized way.At first we review the formulation and outcomes by using it.As a result, in addition to ordinary quantum correlation (Bell pair part), two new types of contribution we call Shannon part and color part, will appear.After outlining this effect explicitly, we analyze entanglement entropy of the ground state for 2-dimensional SU (N ) gauge theory with fundamental scalar matter field.As tools to perform that, we use transfer matrix method and hopping parameter expansion(HPE), roughly the hopping parameter corresponds to inverse square of the mass for the matter.The evaluation is carried out in the perturbation from infinity mass limit.In the analysis, we observe that all of the three types of contribution emerge, while Bell pair part does in higher order than Shannon and color part.We discuss the implication by the result.
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.
We examine the entanglement properties of the Yang-Mills theory by calculating α entanglement entropy with α = 2 using a SU(3) quenched lattice gauge simulation both in the confinement and the deconfinement phases.In the confinement phase, the derivative of the α entropy with respect to the size l of the subregion, whose entanglement properties are interested in, scales as 1/l 3 , and a clear discontinuity cannot be found within our statistical errors.The α entropy in the deconfinement phase saturates at large l.The saturation value is comparable with the thermal entropy of the pure Yang-Mills theory, indicating that the α entropy obeys the volume law at large l in the deconfinement phase.