Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: A comparison with multiparameter reweighting

We study lattice QCD at nonvanishing chemical potential using the complex Langevin equation. We compare the results with multiparameter reweighting both from $\mu =0$ and phase-quenched ensembles. We find a good agreement for lattice spacings below $\approx 0.15\mathrm{fm}$. On coarser lattices the complex Langevin approach breaks down. Four flavors of staggered fermions are used on $N_t=4$, 6 and 8 lattices. For one ensemble we also use two flavors to investigate the effects of rooting.

Figure 1

Comparison of plaquette averages and Polyakov loops and inverse Polyakov loops [defined in and below Eq. (11)] calculated with CLE and reweighting from the $\mu =0$ ensemble.

Figure 2

Comparison of the chiral condensate and fermionic density as well as the phase average (13) calculated with CLE and reweighting from the $\mu =0$ ensemble.

Figure 3

The histogram of the relative weight of the configurations for different chemical potentials.

Figure 4

Comparison of plaquette averages and Polyakov loops calculated with CLE and reweighting from the $\mu =0$ ensemble. We use $N_F=2$ fermion flavors for the data presented in this plot.

Figure 5

Comparison of the plaquette averages and Polyakov loops as a function of $\mu$ at a fixed $\beta =5.4$ calculated with CLE and reweighting from the phase-quenched ensemble.

Figure 6

Comparison of the plaquette averages and Polyakov loops as a function of the $\beta$ parameter at a fixed $\mu /T=1$ calculated with CLE and reweighting from the $\mu =0$ ensemble.

Figure 7

Comparison of the chiral condensate and the fermionic density as a function of the $\beta$ parameter at a fixed $\mu /T=1$ calculated with CLE and reweighting from the $\mu =0$ ensemble.

Figure 8

The histograms of the spatial plaquette variable in the CLE simulation, measured at various $\beta$ values corresponding to Figs. 6 and 7.

Figure 9

Comparison of the plaquette averages and Polyakov loops as a function of the $\beta$ parameter at a fixed $\mu /T=0.72$ calculated with CLE and reweighting from the $\mu =0$ ensemble on ${12}^3\times 6$ lattices.

Figure 10

Comparison of the plaquette averages and Polyakov loops as a function of the $\beta$ parameter at a fixed $\mu /T=0.96$, using $m=0.01$ and $m=0.05$ as indicated, calculated with CLE and reweighting from the $\mu =0$ ensemble on ${16}^3\times 8$ lattices.

Figure 11

Comparison of the fermionic density as a function of the $\beta$ parameter at a fixed $\mu /T=0.96$, using $m=0.01$ and $m=0.05$ as indicated, calculated with CLE and reweighting from the $\mu =0$ ensemble on ${16}^3\times 8$ lattices.