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Register a new userComplex Langevin Dynamics in 1+1d QCD at Non-Zero Densities
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We present our results obtained from gauge cooled complex Langevin simulations in 1+1d QCD at non-zero densities in the strong coupling regime with unrooted staggered fermions. For small quark masses there are regions of the chemical potential where this method fails to reproduce correct results. In these parameter ranges we studied the effect of different gauge cooling schemes on the distributions of the fermion determinant as well as of observables.
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We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with $beta = 5.7$ and four-flavor staggered fermions with degenerate quark mass $m a = 0.01$ and nonzero quark chemical potential $mu$. We confirm that a sufficient condition for correct convergence is satisfied for $mu /T = 5.2 - 7.2$ on a $8^3 times 16$ lattice and $mu /T = 1.6 - 9.6$ on a $16^3 times 32$ lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to $mu$ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) $times$ 4 (flavor) $times$ 2 (spin) $=24$. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.
We present results on the QCD equation of state, obtained with two different improved dynamical staggered fermion actions and almost physical quark masses. Lattice cut-off effects are discussed in detail as results for three different lattice spacings are available now, i.e. results have been obtained on lattices with temporal extent of $N_tau=4,6$ and 8. Furthermore we discuss the Taylor expansion approach to non-zero baryon chemical potential by means of an expansion of the pressure. We use the expansion coefficients to calculate various fluctuations and correlations among hadronic charges. We find that the correlations reproduce the qualitative behavior of the resonance gas model below $T_c$ and start to agree with the free gas predictions for $Tgsim 1.5T_c$.
Partition function zeros provide alternative approach to study phase structure of finite density QCD. The structure of the Lee-Yang edge singularities associated with the zeros in the complex chemical potential plane has a strong influence on the real axis of the chemical potential. In order to investigate what the singularities are like in a concrete form, we resort to an effective theory based on a mean field approach in the vicinity of the critical point. The crossover is identified as a real part of the singular point. We consider the complex effective potential and explicitly study the behavior of its extrema in the complex order parameter plane in order to see how the Stokes lines are associated with the singularity. Susceptibilities in the complex plane are also discussed.
We present results for pseudo-critical temperatures of QCD chiral crossovers at zero and non-zero values of baryon ($B$), strangeness ($S$), electric charge ($Q$), and isospin ($I$) chemical potentials $mu_{X=B,Q,S,I}$. The results were obtained using lattice QCD calculations carried out with two degenerate up and down dynamical quarks and a dynamical strange quark, with quark masses corresponding to physical values of pion and kaon masses in the continuum limit. By parameterizing pseudo-critical temperatures as $ T_c(mu_X) = T_c(0) left[ 1 -kappa_2^{X}(mu_{X}/T_c(0))^2 -kappa_4^{X}(mu_{X}/T_c(0))^4 right] $, we determined $kappa_2^X$ and $kappa_4^X$ from Taylor expansions of chiral observables in $mu_X$. We obtained a precise result for $T_c(0)=(156.5pm1.5);mathrm{MeV}$. For analogous thermal conditions at the chemical freeze-out of relativistic heavy-ion collisions, i.e., $mu_{S}(T,mu_{B})$ and $mu_{Q}(T,mu_{B})$ fixed from strangeness-neutrality and isospin-imbalance, we found $kappa_2^B=0.012(4)$ and $kappa_4^B=0.000(4)$. For $mu_{B}lesssim300;mathrm{MeV}$, the chemical freeze-out takes place in the vicinity of the QCD phase boundary, which coincides with the lines of constant energy density of $0.42(6);mathrm{GeV/fm}^3$ and constant entropy density of $3.7(5);mathrm{fm}^{-3}$.
The WHOT-QCD Collaboration is pushing forward lattice studies of QCD at finite temperatures and densities using improved Wilson quarks. We first present results on QCD at zero and finite densities with two flavors of degenerate quarks (N_F=2 QCD) adopting the conventional fixed-Nt approach. We then report on the status of a study of N_F=2+1 QCD adopting a fixed-scale approach armed with the T-integration method which we have developed.
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