Imaginary Chemical Potential Approach for the Pseudo-Critical Line in the QCD Phase Diagram with Clover-Improved Wilson Fermions

The QCD phase diagram is studied in the lattice QCD simulation with the imaginary chemical potential approach. We employ a clover-improved Wilson fermion action of two-flavors and a renormalization-group improved gauge action, and perform the simulation at an intermediate quark mass on a $8^3\times 4$ lattice. The QCD phase diagram in the imaginary chemical potential $\mu_I$ region is investigated by performing the simulation for more than 150 points on the $(\beta,\mu_I)$ plane. We find that the Roberge-Weiss phase transition at $\mu_I/T=\pi/3$ is first order and its endpoint is second order, which are identified by the phase of the Polyakov loop. We determine the pseudo-critical line from the susceptibility of the Polyakov loop modulus. We find a clear deviation from a linear dependence of the pseudo-critical line on $\mu_I^2$.Comment: 10 pages, 20 figures, 3 tables. Revtex4. References are added and, discussions are sharpene

Wilson Fermion Determinant in Lattice QCD

We present a formula for reducing the rank of Wilson fermions from $4 N_c N_x N_y N_z N_t$ to $4 N_c N_x N_y N_z$ keeping the value of its determinant. We analyse eigenvalues of a reduced matrix and coefficients $C_n$ in the fugacity expansion of the fermion determinant $\sum_n C_n (\exp(\mu/T))^n$, which play an important role in the canonical formulation, using lattice QCD configurations on a $4^4$ lattice. Numerically, $\log |C_n|$ varies as $N_x N_y N_z$, and goes easily over the standard numerical range; We give a simple cure for that. The phase of $C_n$ correlates with the distribution of the Polyakov loop in the complex plain. These results lay the groundwork for future finite density calculations in lattice QCD.Comment: 20 pages, 2 tables, 32 figure

QCD Phase Diagram with Imaginary Chemical Potential

We report our recent results on the QCD phase diagram obtained from the lattice QCD simulation. The location of the phase boundary between hadronic and QGP phases in the two-flavor QCD phase diagram is investigated. The imaginary chemical potential approach is employed, which is based on Monte Carlo simulations of the QCD with imaginary chemical potential and analytic continuation to the real chemical potential region.Comment: Proceedings of Hadron Nuclear Physics (HNP) 2011 on February 21-24, 2011, Pohang, Korea. MSN-011. 8pages, 18figure