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We study the phase structure of imaginary chemical potential. We calculate the Polyakov loop using clover-improved Wilson action and renormalization improved gauge action. We obtain a two-state signals indicating the first order phase transition for $beta = 1.9, mu_I = 0.2618, kappa=0.1388$ on $8^3times 4$ lattice volume We also present a result of the matrix reduction formula for the Wilson fermion.
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The order of the thermal transition in the chiral limit of QCD with two dynamical flavours of quarks is a long-standing issue. Still, it is not definitely known whether the transition is of first or second order in the continuum limit. Which of the two scenarios is realized has important implications for the QCD phase diagram and the existence of a critical endpoint at finite densities. Settling this issue by simulating at successively decreased pion mass was not conclusive yet. Recently, an alternative approach was proposed, extrapolating the first order phase transition found at imaginary chemical potential to zero chemical potential with known exponents, which are induced by the Roberge-Weiss symmetry. For staggered fermions on $N_t=4$ lattices, this results in a first order transition in the chiral limit. Here we report of $N_t=4$ simulations with Wilson fermions, where the first order region is found to be large.
The order of the thermal phase transition in the chiral limit of Quantum Chromodynamics (QCD) with two dynamical flavors of quarks is a long-standing issue and still not known in the continuum limit. Whether the transition is first or second order has important implications for the QCD phase diagram and the existence of a critical endpoint at finite densities. We follow a recently proposed approach to explicitly determine the region of first order chiral transitions at imaginary chemical potential, where it is large enough to be simulated, and extrapolate it to zero chemical potential with known critical exponents. Using unimproved Wilson fermions on coarse $N_t=4$ lattices, the first order region turns out to be so large that no extrapolation is necessary. The critical pion mass $m_pi^capprox 560$ MeV is by nearly a factor 10 larger than the corresponding one using staggered fermions. Our results are in line with investigations of three-flavour QCD using improved Wilson fermions and indicate that the systematic error on the two-flavour chiral transition is still of order 100%.
We investigate chemical-potential ($mu$) dependence of the static-quark free energies in both the real and imaginary $mu$ regions, using the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. Static-quark potentials are evaluated from Polyakov-loop correlators in the deconfinement phase and the imaginary $mu=imu_{rm I}$ region and extrapolated to the real $mu$ region with analytic continuation. As the analytic continuation, the potential calculated at imaginary $mu=imu_{rm I}$ is expanded into a Taylor-expansion series of $imu_{rm I}/T$ up to 4th order and the pure imaginary variable $imu_{rm I}/T$ is replaced by the real one $mu_{rm R}/T$. At real $mu$, the 4th-order term weakens $mu$ dependence of the potential sizably. Also, the color-Debye screening mass is extracted from the color-singlet potential at imaginary $mu$, and the mass is extrapolated to real $mu$ by analytic continuation. The screening mass thus obtained has stronger $mu$ dependence than the prediction of the leading-order thermal perturbation theory at both real and imaginary $mu$.
Wilson Fermions with untwisted and twisted mass are widely used in lattice simulations. Therefore one important question is whether the twist angle and the lattice spacing affect the phase diagram. We briefly report on the study of the phase diagram of QCD in the parameter space of the degenerate quark masses, isospin chemical potential, lattice spacing, and twist angle by employing chiral perturbation theory. Moreover we calculate the pion masses and their dependence on these four parameters.
Using GPGPU techniques and multi-precision calculation we developed the code to study QCD phase transition line in the canonical approach. The canonical approach is a powerful tool to investigate sign problem in Lattice QCD. The central part of the canonical approach is the fugacity expansion of the grand canonical partition functions. Canonical partition functions $Z_n(T)$ are coefficients of this expansion. Using various methods we study properties of $Z_n(T)$. At the last step we perform cubic spline for temperature dependence of $Z_n(T)$ at fixed $n$ and compute baryon number susceptibility $chi_B/T^2$ as function of temperature. After that we compute numerically $partialchi/ partial T$ and restore crossover line in QCD phase diagram. We use improved Wilson fermions and Iwasaki gauge action on the $16^3 times 4$ lattice with $m_{pi}/m_{rho} = 0.8$ as a sandbox to check the canonical approach. In this framework we obtain coefficient in parametrization of crossover line $T_c(mu_B^2)=T_cleft(c-kappa, mu_B^2/T_c^2right)$ with $kappa = -0.0453 pm 0.0099$.
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