The QCD phase diagram for small densities from imaginary chemical potential

TL;DR

This paper develops a controllable lattice approach to the QCD phase diagram at small baryon densities by simulating with an imaginary chemical potential $\mu_I$, where the fermion determinant is positive. The authors show that the (pseudo-)critical line $\beta_c(\mu)$ is analytic in $\mu$ near zero and can be expanded in $\mu^2$, enabling analytic continuation from $\mu_I$ to real $\mu$ within the region $|\mu|\leq \pi/3$. On an $8^3\times4$ lattice with two light flavors, they map the $Z(3)$ transition and the deconfinement transition as functions of $\mu_I$, find that the data are best described by a leading $\mu_I^2$ term with higher orders negligible, and translate the deconfinement line to physical units to obtain $T_c(\mu)/T_c(0) = 1 - 0.00563(38)(\mu_B/T)^2$ up to $\mu_B \sim 500$ MeV. The results provide a systematic, reweighting-free route to the small-density QCD phase diagram, corroborate with other methods within uncertainties, and highlight the importance of finite-volume and continuum extrapolations for precision.

Abstract

We present results on the QCD phase diagram for mu_B <= pi T. Our simulations are performed with an imaginary chemical potential mu_I for which the fermion determinant is positive. On an 8^3 x 4 lattice with 2 flavors of staggered quarks, we map out the phase diagram and identify the pseudo-critical temperature T_c(mu_I). For mu_I/T <= pi/3, this is an analytic function, whose Taylor expansion is found to converge rapidly, with truncation errors far smaller than statistical ones. The truncated series may then be continued to real mu, yielding the corresponding phase diagram for mu_B <~ 500 MeV. This approach provides control over systematics and avoids reweighting. We compare it with other recent work.

Figures (10)

• Figure 1: Location of $Z(3)$ transitions, Eq. (\ref{['zcrit']}). Analytic continuation is limited to the region within the arc.
• Figure 2: Schematic location of the lines defined by Eq. (\ref{['crit1']}). In the infinite volume limit (right), the lines merge for a phase transition, but stay separate for a crossover, the bifurcation marking the end point of the phase transition.
• Figure 3: Probability distribution of the phase of the Polyakov loop for the critical value $a\mu_I^c=\pi/12$.
• Figure 4: The $\beta$- and $\mu_I$-dependence of the average phase of the Polyakov loop.
• Figure 5: Schematic phase diagram for imaginary chemical potential: The vertical line marks the $Z(3)$ transition (this section), the curved lines the deconfinement transition (next section). The solid line indicates a first order transition, while the nature of the dotted lines is not yet determined. The diagram is periodically repeated for larger values of $\mu_I$.