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Register a new userDual simulation of a Polyakov loop model at finite baryon density: phase diagram and local observables
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Many Polyakov loop models can be written in a dual formulation which is free of sign problem even when a non-vanishing baryon chemical potential is introduced in the action. Here, results of numerical simulations of a dual representation of one such effective Polyakov loop model at finite baryon density are presented. We compute various local observables such as energy density, baryon density, quark condensate and describe in details the phase diagram of the model. The regions of the first order phase transition and the crossover, as well as the line of the second order phase transition, are established. We also compute several correlation functions of the Polyakov loops.
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Neither the chiral limit nor finite baryon density can be simulated directly in lattice QCD, which severely limits our understanding of the QCD phase diagram. In this review I collect results for the phase structure in an extended parameter space of QCD, with varying numbers of flavours, quark masses, colours, lattice spacings, imaginary and isospin chemical potentials. Such studies help in understanding the underlying symmetries and degrees of freedom, and are beginning to provide a consistent picture constraining the possibilities for the physical phase diagram.
We investigate the Polyakov loop effects on the QCD phase diagram by using the strong-coupling (1/g^2) expansion of the lattice QCD (SC-LQCD) with one species of unrooted staggered quark, including O}(1/g^4) effects. We take account of the effects of Polyakov loop fluctuations in Weiss mean-field approximation (MFA), and compare the results with those in the Haar-measure MFA (no fluctuation from the mean-field). The Polyakov loops strongly suppress the chiral transition temperature in the second-order/crossover region at small chemical potential, while they give a minor modification of the first-order phase boundary at larger chemical potential. The Polyakov loops also account for a drastic increase of the interaction measure near the chiral phase transition. The chiral and Polyakov loop susceptibilities have their peaks close to each other in the second-order/crossover region. In particular in Weiss MFA, there is no indication of the separated deconfinement transition boundary from the chiral phase boundary at any chemical potential. We discuss the interplay between the chiral and deconfinement dynamics via the bare quark mass dependence of susceptibilities.
We revisit the Polyakov Loop coupled Nambu-Jona-Lasinio model that maintains the Polyakov loop dynamics in the limit of zero temperature. This is of interest for astrophysical applications in the interior of neutron stars. For this purpose we re-examine the form of the potential for the deconfinement order parameter at finite baryonic densities. Since the modification of this potential at any temperature is formally equivalent to assigning a baryonic charge to gluons, we develop a more general formulation of the present model that cures this spurious effect and is normalized to match the asymptotic behaviour of the QCD equation of state given by $mathcal{O}(alpha_s^2)$ and partial $mathcal{O}(alpha_s^3ln^2alpha_s)$ perturbative results.
The phase structure of two-flavor QCD is explored for thermal systems with finite baryon- and isospin-chemical potentials, mu_B and mu_{iso}, by using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. The PNJL model with the scalar-type eight-quark interaction can reproduce lattice QCD data at not only mu_{iso}=mu_B=0 but also mu_{iso}>0 and mu_B=0. In the mu_{iso}-mu_{B}-T space, where T is temperature, the critical endpoint of the chiral phase transition in the mu_B-T plane at mu_{iso}=0 moves to the tricritical point of the pion-superfluidity phase transition in the mu_{iso}-T plane at mu_B=0 as mu_{iso} increases. The thermodynamics at small T is controlled by sqrt{sigma^2+pi^2} defined by the chiral and pion condensates, sigma and pi.
We study genuine finite density effects in QCD-like theories with three-dimensional Polyakov-loop effective theories for heavy quarks. These are derived from the full QCD-like theories by combined strong-coupling and hopping expansions. In particular, we investigate the cold and dense regimes of phase diagrams where we expect to find Bose-Einstein-condensation of diquark baryons or a fermionic first-order liquid-gas transition, depending on the gauge group of the theory. In two-color QCD, for example, we observe evidence of a continuous zero-temperature transition to finite diquark density when the quark chemical potential $mu$ reaches half the diquark mass, i.e. without binding energy. In G$_2$-QCD we observe, in addition to this Silver Blaze onset of diquark density, a second transition in the density towards an exponential increase by roughly $3mu/T$ corresponding to a finite density of G$_2$-nucleons.
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