Phase diagram of a gauge theory with fermionic baryons

The fermion-sign problem at finite density is a persisting challenge for Monte Carlo simulations. Theories that do not have a sign problem can provide valuable guidance and insight for physically more relevant ones that do. Replacing the gauge group SU(3) of QCD by the exceptional group ${\mathrm{G}}_2$, for example, leads to such a theory. It has mesons as well as bosonic and fermionic baryons, and shares many features with QCD. This makes the ${\mathrm{G}}_2$ gauge theory ideally suited to study general properties of dense, strongly interacting matter, including baryonic and nuclear Fermi pressure effects. Here we present the first-ever results from lattice simulations of ${\mathrm{G}}_2$ QCD with dynamical fermions, providing a first explorative look at the phase diagram of this QCD-like theory at finite temperature and baryon chemical potential.

Figure 1

The left panel shows an example for the mass correlator fits performed. Since in most cases no clear mass plateaus appear due to closeness of the excited states, conservative error estimates have been used, which are shown in the example as error bands. The right panel shows the masses obtained in this way. Note the shifted $\beta$ values to disentangle the plot. All results are for $\kappa =0.15625$. Only the range $\beta =0.9$ to $\beta =1.0$ has been used in the phase diagram calculations.

Figure 2

The Polyakov loop and the unrenormalized chiral condensate at zero chemical potential (left panel) and the renormalized chiral condensate (right panel).

Figure 3

Bottom row: Raw Polyakov loop data (left), chiral condensate (middle), and normalized baryon density (right) at finite quark chemical potential $\mu$ and temperatures $T=0$, 98 and 131 MeV. Top row: Corresponding numerical derivatives.

Figure 4

The data from the bottom row of Fig. 3 in lattice units.

Figure 5

Interpolated phase diagram for the Polyakov loop (left), chiral condensate (middle), and baryon density (right).