Two-colour QCD phases and the topology at low temperature and high density

Abstract

We delineate equilibrium phase structure and topological charge distribution of dense two-colour QCD at low temperature by using a lattice simulation with two-flavour Wilson fermions that has a chemical potential µ and a diquark source j incorporated. We systematically measure the diquark condensate, the Polyakov loop, the quark number density and the chiral condensate with improved accuracy and j → 0 extrapolation over earlier publications; the known qualitative features of the low temperature phase diagram, which is composed of the hadronic, Bose-Einstein condensed (BEC) and BCS phases, are reproduced. In addition, we newly find that around the boundary between the hadronic and BEC phases, nonzero quark number density occurs even in the hadronic phase in contrast to the prediction of the chiral perturbation theory (ChPT), while the diquark condensate approaches zero in a manner that is consistent with the ChPT prediction. At the highest µ, which is of order the inverse of the lattice spacing, all the above observables change drastically, which implies a lattice artifact. Finally, at temperature of order 0.45T c , where T c is the chiral transition temperature at zero chemical potential, the topological susceptibility is calculated from a gradient-flow method and found to be almost constant for all the values of µ ranging from the hadronic to BCS phase. This is a contrast to the case of 0.89T c in which the topological susceptibility becomes small as the hadronic phase changes into the quark-gluon plasma phase.

Lattice study of thermodynamic properties of dense QC2D

“…To proceed we fit simultaneously our lattice data for the diquark condensate, the chiral condensate and the quark number density in the region aμ ∈ ð0; 0.12Þ by modified formulas 22 quite well, we conclude that at low density (μ < 540 MeV) the system under study is well described by ChPT. A similar conclusion was also drawn in papers [29,32,33].…”

“…The two-color QCD at finite chemical potential has been studied with lattice simulations quite intensively, see, e.g., [24][25][26][27][28][29][30][31][32][33][34][35] and references therein. Mostly, these papers are aiming at the study of the phase diagram of two-color QCD in the region of small and moderate baryon densities.…”

Dense two-color QCD towards continuum and chiral limits

“…The system was found to be confined at low temperature, with deconfinement only setting in at much larger chemical potential [21]. Similar conclusions were found in [23]. It is also worth noting that a recent study of QCD with nonzero isospin chemical potential [5] found a phase diagram very similar to that of [8], namely a pion condensed phase at low T and large µ, with a critical temperature that is nearly independent of µ, and a deconfinement transition line that intersects with the pion condensation transition.…”

“…There remain significant uncertainties relating to the extrapolation to zero diquark source j, with our data unable to distinguish between a linear j-dependence and the nonanalytic behaviour expected at least in the vicinity of the onset transition. This may be mitigated by adopting the reweighting method introduced in [5] and implemented in the context of QC 2 D in [23]; this will be left for future investigations.…”

“…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.…”