Phase diagram of QCD at finite temperature and chemical potential from lattice simulations with dynamical Wilson quarks

We present the first results for lattice QCD at finite temperature $T$ and chemical potential $\mu$ with four flavors of Wilson quarks. The calculations are performed using the imaginary chemical potential method at $\kappa =0,0.001,0.15,0.165,0.17\mathrm{and}0.25$, where $\kappa$ is the hopping parameter, related to the bare quark mass $m$ and lattice spacing $a$ by $\kappa =1/(2ma+8)$. Such a method allows us to do large scale Monte Carlo simulations at imaginary chemical potential $\mu =i{\mu }_I$. By analytic continuation of the data with ${\mu }_I<\pi T/3$ to real values of the chemical potential, we expect at each $\kappa \in [0,{\kappa }_{\mathrm{chiral}}]$, a phase transition line on the $(\mu ,T)$ plane, in a region relevant to the search for quark-gluon plasma in heavy-ion collision experiments. The transition is first order at small or large quark mass, and becomes a crossover at intermediate quark mass.

Figure 1

Schematic phase diagram of QCD on the $({\mu }_I,T)$ plane, suggested by Roberge and Weiss. For $T\ge T_E$, there are first order phase transitions at $a{\mu }_I=2\pi (k+1/2)/N$, characterized by discontinuity in the Polyakov loop. Here $N=N_c{N}_t$ and $N_{t}a=1/T$. [There is no phase transition across the dashed lines; they just illustrate the location of $T_E$ or $a{\mu }_I=2\pi (k+1/2)/N$.

Figure 2

Schematic phase diagram of QCD on the $({\mu }_I,T)$ plane, suggested by lattice MC study.

Figure 3

Polyakov loop norm as a function of $a{\mu }_I$ at $\kappa =0.15$ and two different $\beta$.

Figure 4

Chiral condensate as a function of $a{\mu }_I$ at $\kappa =0.15$ and two different $\beta$.

Figure 5

Phase of the Polyakov loop as a function of $a{\mu }_I$ at $\beta =5.25$ and $\kappa =0.15$.

Figure 6

MC history of the phase of the Polyakov loop at $a{\mu }_I=0.26$, $\beta =5.25$, and $\kappa =0.15$.

Figure 7

Chiral condensate as a function of $\beta$ at $\kappa =0.15$ and two different values of $a{\mu }_I$.

Figure 8

Chiral susceptibility as a function of $\beta$ at $\kappa =0.15$ and two different values of $a{\mu }_I$.

Figure 9

Polyakov loop norm as a function of $\beta$ at $\kappa =0.15$ and two different $a{\mu }_I$.

Figure 10

Susceptibility of the Polyakov loop norm as a function of $\beta$ at $\kappa =0.15$ and two different $a{\mu }_I$.

Figure 11

Susceptibility of the Polyakov loop norm as a function of $\beta$ at $a{\mu }_I=0.14$ and $\kappa =0.15$ for different spatial volumes $V=8^3$ and ${12}^3$.

Figure 12

Susceptibility of the Polyakov loop norm as a function of the spacial extent $L$ at $a{\mu }_I=0.14$, $\beta =5.187$ and $\kappa =0.15$.

Figure 13

Histogram of the Polyakov loop norm at and $a{\mu }_I=0.1$, $\beta =4.87$ and $\kappa =0.165$.

Figure 14

MC history of the Polyakov loop norm at $a{\mu }_I=0.1$, $\beta =4.87$, and $\kappa =0.165$.

Figure 15

MC history of the Polyakov loop norm at $a{\mu }_I=0.1$, $\beta =5.691$, and $\kappa =0$.

Figure 16

MC history of the Polyakov loop norm at $a{\mu }_I=0.1$, $\beta =5.68$, and $\kappa =0.001$.

Figure 17

MC history of the Polyakov loop norm at $a{\mu }_I=0.1$, $\beta =4.736$, and $\kappa =0.17$.

Figure 18

Chiral condensate susceptibility as a function of $\beta$ at $a{\mu }_I=0.1$ and $\kappa =0.25$.

Figure 19

Susceptibility of the Polyakov loop norm as a function of $\beta$ at $a{\mu }_I=0.1$ and $\kappa =0.25$.

Figure 20

Phase diagram on the $(\mu ,T)$ plane for $\kappa =0.15$. The area between the two solid lines is our result for Wilson quarks with error band, derived from Eqs. (13, 14). The area between the two dotted lines is the result for KS fermions by D’Elia and Lombardo.

Figure 21

Expected phase diagram of lattice QCD with four flavors of Wilson quarks in the $(\mu ,T,\kappa )$ parameter space. For $\kappa \in [0,{\kappa }_1]$ and $\kappa \in [{\kappa }_2,{\kappa }_{\mathrm{chiral}}]$, the phase transition is of first order, and while for $\kappa \in ({\kappa }_1,{\kappa }_2)$, the transition is a crossover.