QCD phase diagram for nonzero isospin-asymmetry

Abstract

The QCD phase diagram is studied in the presence of an isospin asymmetry using continuum extrapolated staggered quarks with physical masses. In particular, we investigate the phase boundary between the normal and the pion condensation phases and the chiral/deconfinement transition. The simulations are performed with a small explicit breaking parameter in order to avoid the accumulation of zero modes and thereby stabilize the algorithm. The limit of vanishing explicit breaking is obtained by means of an extrapolation, which is facilitated by a novel improvement program employing the singular value representation of the Dirac operator. Our findings indicate that no pion condensation takes place above T ≈ 160 MeV and also suggest that the deconfinement crossover continuously connects to the BEC-BCS crossover at high isospin asymmetries. The results may be directly compared to effective theories and model approaches to QCD.

Dense two-color QCD towards continuum and chiral limits

“…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.…”

“…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.…”

“…The problem may be circumvented by studying QCDlike theories without a sign problem, such as theories with adjoint fermions in any gauge group, QCD with isospin chemical potential [5], or QCD with gauge groups SU(2) (QC 2 D) [6][7][8] or G 2 (G 2 -QCD) [9,10]. Although these theories all have qualitative features which distinguish them from real QCD at nonzero baryon chemical potential -notably a gauge-invariant Bose-Einstein condensate (BEC) above an onset chemical potential µ o -they share salient features such as spontaneous chiral symmetry breaking and confinement at T = µ = 0, and may be used as laboratories for strongly interacting theories at high density.…”

Chiral density wave versus pion condensation at finite density and zero temperature

“…Again there will be finite corrections to μ I ¼ 1 2 m π and in some cases, the deviation can be substantial [35]. Finally, we mention that the lattice result [13][14][15] for the onset of pion condensation at T ¼ 0 for 2 þ 1 dynamical quarks is in agreement with this. Likewise, their simulations strongly suggest that the transition is second order in the Oð2Þ universality class in agreement with expectations.…”

“…Systems at zero baryon chemical potential and finite isospin chemical potential are of particular interest, since the fermion determinant is real and one can perform lattice simulations using standard importance sampling techniques, see e.g. [11][12][13][14][15]. The picture that emerges from the simulations is that at T ¼ 0, the chiral condensate is constant for μ I below a critical value, μ c I ¼ 1 2 m π .…”