Exact center symmetry and first-order phase transition in QCD with three degenerate dynamical quarks

Abstract

We study QCD with three degenerate flavors of dynamical quarks using first-principles lattice simulations. For a specific choice of imaginary isospin chemical potential, this theory possesses an exact center symmetry, just like pure gauge theory. This exact symmetry is expected to be intact at low temperatures and spontaneously broken in the high-temperature regime. By analyzing the finite-size scaling of the Polyakov loop distribution, obtained with a dedicated multi-histogram approach, we demonstrate that there is a first-order deconfinement phase transition in between. Our results are obtained employing stout-smeared rooted staggered quarks at one lattice spacing. Using simulations at different quark masses we sketch the behavior of QCD in the mass-isospin chemical potential plane, shedding new light on this corner of the fundamental phase diagram of the strong interactions and the relationship between chiral symmetry breaking and deconfinement.

Figures (9)

• Figure 1: Phase diagram of QCD with three massless quark flavors in the $i\mu_u-i\mu_d$ plane at $\mu_s=0$. The colors indicate the three center sectors, where the Polyakov loop phase is real (black) positive imaginary (yellow/light) or negative imaginary (blue/medium). The red dots indicate $\mathrm{Z}(3)$-symmetric points. Opposite edges of the diagram are identified due to the periodicity in the imaginary chemical potentials. The case of a pure isospin chemical potential is described by points along the diagonal from the top-left to the bottom-right corner. One of the two triple points matches the triple point identified in \ref{['eq:imagiso_choice']} after shifting the negative-valued chemical potential up by $2 \pi T$ and the second one is a result of exchanging the up- and down-values.
• Figure 2: Monte Carlo history of the real (gold) and imaginary (blue) part of the Polyakov loop on a $16^3\times 6$ ensemble at high temperature. Frequent jumps between the center sectors are observed.
• Figure 4: Histogram of the rotated Polyakov loop on our $16^3\times6$ ensembles, with the same color coding for the temperatures as in \ref{['fig:ploop_hist2']}.
• Figure 6: Moments of the distribution of the rotated Polyakov loop as a function of $\beta$ for different volumes. The panels show $\langle \bar{P}\rangle$ (top left), $\kappa_2$ (bottom left), $s_{\bar{P}}$ (top right) and $B_{\bar{P}}$ (bottom right).
• Figure 7: Expectation value of the quark condensate as a function of $\beta$ for different volumes.