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