The entanglement at finite temperatures are analyzed by using thermal models for colored quarks making up the hadron physical states. We have found that these quantum correlations entirely vanish at
Tc≥mq/ln(1.5). For temperatures larger than
Tc the correlations are classical. Also we worked out the entanglement for the transverse Ising spin chain. In dependence on both temperature
T and transverse field
λ we can identify a certain region, where the quantum effects are likely to dominate the system. We suggest the mutual information as a quantitative measure for the correlations in ground state.
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.
We look at two well known examples of interacting systems relating to condensed matter in which we put the strong interacting parameters. At high quark chemical potentials and low temperatures we study the entropy arising from the excitation in the BCS model of superconductivity and the Bose-Einstein condensation (BEC) of colored quark pairs. We compare it with the ground state entropy for a system consisting of two colored quarks. In the BCS model we found that the entropy strongly depends on the energy gap. Both for the very small values of the momenta as well as those much greater than the characterizing Fermi momentum
pf, the ground state entropy is dominant. For the BEC case we suggest a phenomenological model to build up colored bosonic quark pairs. Here the entropy entirely depends upon the short ranged repulsive interactions between the quark pairs and vanishes for large momenta.
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.
The modulation is analyzed from the analytical properties of zeros of the free fermionic partition function on the complex plane of wave numbers. It is shown how these properties are related to the oscillations of correlation functions. This approach can be used for analysis of phase transitions with local or nonlocal order parameters, as well as for the disorder lines. We find an infinite cascade of disorder lines at finite temperature in the quantum
XY chain (equivalent to free fermions). The well-known ground-state factorization on the disorder line, and consequently disentanglement, is shown to follow directly from analytical properties of this model on the complex plane. From the quantum-classical correspondence the results for the chain are used to detect the disorder lines in several frustrated two-dimensional Ising models. The present formalism can be applied to other fermionic models in two and three spatial dimensions. In particular, we find the temperature-dependent Fermi wave vector of oscillations in the degenerate gas of three-dimensional fermions, which naturally leads in the limit $T\ensuremath{\rightarrow}0$ to the definition of the Fermi energy as the surface of quantum criticality. The modulation is a very common phenomenon, and it occurs in a large variety of models. The important point is that all these modulation transitions can be related to the complex zeros of partition functions, as done in the present study.