Towards the phase diagram of dense two-color matter

Abstract

We study two-color QCD with two flavors of Wilson fermion as a function of quark chemical potential µ and temperature T . We find evidence of a superfluid phase at intermediate µ and low T where the quark number density and diquark condensate are both very well described by a Fermi sphere of nearly-free quarks disrupted by a BCS condensate. Our results suggest that the quark contribution to the energy density is negative (and balanced by a positive gauge contribution), although this result is highly sensitive to details of the energy renormalisation. We also find evidence that the chiral condensate in this region vanishes in the massless limit. This region gives way to a region of deconfined quark matter at higher T and µ, with the deconfinement temperature, determined from the renormalised Polyakov loop, decreasing only very slowly with increasing chemical potential. The quark number susceptibility χq does not exhibit any qualitative change at the deconfinement transition. We argue that this is because χq is not an appropriate measure of deconfinement for 2-color QCD at high density.

Phase diagram of dense two-color QCD within lattice simulations

“…It is interesting to note, that this fit gives a satisfactory description of the data up to µ ∼ 1055 MeV (µa ∼ 0.6). Thus, one sees that the chiral condensate drops slower with increasing chemical potential than ChPT predicts (similar slower decrease of the form qq ∼ 1/µ was observed in [21] with N f = 2 Wilson quarks). Figure 3.…”

“…The main activity in two-color QCD was later continued by the Swansea group (S. Hands and collaborators) for the two-flavor theory with Wilson fermions [19][20][21][22]. In a low temperature scan of the phase diagram the authors observed a hadronic phase, followed by the BCS phase with deconfinement, but did not encounter the BEC phase.…”

Lattice simulation of $QC_2D$ with $N_f=2$ at non-zero baryon density

“…Especially interesting is to understand the effect of a non-zero baryon density on the breaking/recovery of the chiral symmetry. Similar investigations were performed in [3,5,6] for N f = 2 with Wilson fermions and in [7] [8] with N f = 4 and 8 flavors of staggered fermions respectively. However, Wilson fermions explicitly violate the chiral symmetry [9], thus they may not reveal all the phase transition lines in the QC 2 D phase diagram.…”

Strong interaction effects at a Fermi surface in a model for voltage-biased bilayer graphene

“…In [13] the gap in the 3 + 1d Nambu Jona-Lasinio model (a relativistic analog of the original BCS model) was shown to be approximately constant above onset, independent of and numerically much smaller than μ, consistent with the BCS result ∼ UV exp(−c 2 UV /μ 2 ). In QCD with gauge group SU(2) there is a so-called quarkyonic regime above onset where ∝ μ 2 [16]; this is consistent with degenerate fermions in 3 + 1d with a gap ∼ O( QCD ) independent of μ. It is also very different from the result /μ ∼ O(10 −7 ) obtained by self-consistent diagrammatic techniques [7], although comparable with the large values of /μ obtained in [5], where it was found that depends sensitively on the treatment of screening effects, and in particular on the reduction of screening once the superfluid gap forms.…”

“…In the region of μ studied it is clear that varies strongly with and is of the same order of magnitude as the chemical potential μ, which are notable features of this particular model proposed in [1], and indicative of strong interactions at the Fermi surface. This conclusion holds in both normal and anomalous channels, appears to be independent of volume, and is striking enough to be robust against uncertainties introduced by the ad hoc nature of our analysis [an analytic form against which to fit the dispersion E(k) would be very valuable], the IR and UV artifacts inherent in studies of lattice models with μ = 0 [16], and lack of knowledge of the physical anisotropy a t /a s . On the basis of the three chemical potentials studied both and k F appear to scale superlinearly with μ, in qualitative agreement with (10).…”