Study of the phase diagram of dense two-color QCD within lattice simulation

Abstract

In this paper we carry out a low-temperature scan of the phase diagram of dense two-color QCD with N f = 2 quarks. The study is conducted using lattice simulation with rooted staggered quarks. At small chemical potential we observe the hadronic phase, where the theory is in a confining state, chiral symmetry is broken, the baryon density is zero and there is no diquark condensate. At the critical point µ = mπ/2 we observe the expected second order transition to Bose-Einstein condensation of scalar diquarks. In this phase the system is still in confinement in conjunction with non-zero baryon density, but the chiral symmetry is restored in the chiral limit. We have also found that in the first two phases the system is well described by chiral perturbation theory. For larger values of the chemical potential the system turns into another phase, where the relevant degrees of freedom are fermions residing inside the Fermi sphere, and the diquark condensation takes place on the Fermi surface. In this phase the system is still in confinement, chiral symmetry is restored and the system is very similar to the quarkyonic state predicted by SU(Nc) theory at large Nc.

Dense two-color QCD towards continuum and chiral limits

“…These have to a large extent confirmed the picture outlined above, with some additions. Notably, in [20], with a smaller pion mass than in [6][7][8], a BEC region was found where the diquark condensate and quark number density agree with predictions from chiral perturbation theory, followed by a transition to a quarkyonic region at higher µ. Also, the chiral condensate was found to vanish in the chiral limit in both the BEC and quarkyonic regions.…”

“…The apparent linear j-dependence at all µ may be an indication that non-analytic behaviour only sets in at lower j-values than we have here. To improve on the diquark source extrapolation, it may be necessary to carry out a reweighting procedure as outlined in [5], or explore much smaller values of the source ja [20]. At T = 90 MeV (N τ = 16) we see that qq is significantly smaller for all values of µ, suggesting that this temperature is near the critical temperature for the superfluid to normal phase transition.…”

“…Although we find a deconfinement transition at high temperature, the deconfinement transition previously seen at low T and high µ appears to be a lattice artefact -at T ∼ 45 MeV the Polyakov loop appears to increase from zero at µa ∼ 0.8 for all lattice parameters. Simulations using staggered fermions at a relatively high temperature T > 100 MeV [20,21] have found a deconfinement transition at µ ≈ 750 MeV characterised by the string tension dropping to zero. This is not in contradiction with the absence of any deconfinement transition at T ≈ 45 MeV.…”

“…There have been a number of other lattice studies of dense QC 2 D in recent years, using staggered [20][21][22] and Wilson [23] fermions. These have to a large extent confirmed the picture outlined above, with some additions.…”

Phase diagram of dense two-color QCD within lattice simulations

“…To study the phase diagram of QC 2 D with N f = 2 flavors we used a 16 3 × 32 lattice, simulating with β = 2.15, ma = 0.005, the lattice spacing a = 0.112(1) fm and the pion mass M π = 378(4) MeV (detailed description of the action and parameters may be found in [27]). …”