We study the entanglement of gluon fields in presence of a static
QQˉ pair in quenched QCD. Using the replica method, we investigate the
q=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 consider entanglement entropy between regions of space in lattice gauge theory. The Hilbert space corresponding to a region of space includes ``edge states'' that transform nontrivially under gauge transformations. By decomposing the edge states in irreducible representations of the gauge group, the entropy of an arbitrary state is expressed as the sum of three positive terms: a term associated with the classical Shannon entropy of the distribution of boundary representations, a term that appears only for non-Abelian gauge theories and depends on the dimension of the boundary representations, and a term representing nonlocal correlations. The first two terms are the entropy of the edge states, and depend only on observables measurable at the boundary. These results are applied to several examples of lattice gauge theory states, including the ground state in the strong coupling expansion of Kogut and Susskind. In all these examples we find that the entropy of the edge states is the dominant contribution to the entanglement entropy.
We calculate the entanglement entropy of a model proton wave function in coordinate space by integrating out degrees of freedom outside a small circular region
A of radius
L, where
L is much smaller than the size of the proton. The wave function provides a nonperturbative distribution of three valence quarks. In addition, we include the perturbative emission of a single gluon and calculate the entanglement entropy of gluons in
A. For both quarks and gluons, we obtain the same simple result: ${S}_{E}=\ensuremath{-}\ensuremath{\int}\frac{dx}{\mathrm{\ensuremath{\Delta}}x}{N}_{{L}^{2}}(x)\mathrm{log}[{N}_{{a}^{2}}(x)]$, where
a is the UV cutoff in coordinate space and $\mathrm{\ensuremath{\Delta}}x$ is the longitudinal resolution scale. Here
NS(x) is the number of partons (of the appropriate species) with longitudinal momentum fraction
x inside an area
S. It is related to the standard parton distribution function by ${N}_{S}(x)=\frac{S}{{A}_{p}}\mathrm{\ensuremath{\Delta}}xF(x)$, where
Ap denotes the transverse area of the proton.
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 this analytical mean-field study we construct and analyze a chiral SU(3) spin model on the bi- partite honeycomb lattice. Assigning the fundamental and antifundamental representations of SU(3) to the two sublattices, as required to form a singlet on every bond, together with the choice N = 3, fixes the on-site degree of freedom to a qutrit and the two-site coupling to the SU(3) Heisenberg exchange. By a standard representation-theoretic argument, the single-site reduced entropy equals ln 3 exactly in any finite-size singlet ground state. We show that the natural make-before-break ring exchange around a hexagonal plaquette must advance the site states by two positions to respect the alternation of conjugate representations, and that its time-reversal-odd part decomposes exactly into SU(3) scalar chiralities on the two sublattice triangles of the hexagon, leaving a one-parameter model. A fermionic parton mean-field analysis, with a single U(1) gauge constraint, places the parton bands at the Heisenberg point in a topologically trivial gapped state and shows, through an explicit Wick decoupling of the six-site ring exchange, that the chiral term generates a competing Haldane flux; enforcing the constraint self-consistently, the gap inverts beyond a finite coupling into a phase in which each of the three color bands carries unit Chern number. Integrating out the partons yields an SU(3)1 chiral spin liquid. The candidate phase carries total quantum dimension√3, three anyon sectors with Z3 fusion, chiral central charge two, and topological entanglement entropy ln √3. We present the exact operator identities as an algebraic foundation, and the SU(3)1 identification as a mean-field prediction, for future high-performance tensor-network investigations, which we identify as the necessary test of the proposed phase.
We calculate the entanglement entropy using a SU(3) quenched lattice gauge simulation. We find that the entanglement entropy scales as
1/l2 at small
l as in the conformal field theory. Here
l is the size of the system, whose degrees of freedom is left after the other part are traced out. The derivative of the entanglement entropy with respect to
l hits zero at about
l∗=0.6∼0.7 [fm] and vanishes above the length. It may imply that the Yang-Mills theory has the mass gap of the order of
1/l∗. Within our statistical errors, no discontinuous change can be seen in the entanglement entropy. We discuss also a subtle point appearing in gauge systems when we divide a system with cuts.