We investigate chemical-potential (mu) dependence of static-quark free energies in both the real and imaginary mu regions, performing lattice QCD simulations at imaginary mu and extrapolating the results to the real mu region with analytic continuati
on. Lattice QCD calculations are done on a 16^{3}times 4 lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. Static-quark potential is evaluated from the Polyakov-loop correlation functions in the deconfinement phase. 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. At long distance, all of the color singlet and non-singlet potentials tend to twice the single-quark free energy, indicating that the interactions between heavy quarks are fully color-screened for finite mu. For both real and imaginary mu, the color-singlet q{bar q} and the color-antitriplet qq interaction are attractive, whereas the color-octet q{bar q} and the color-sextet qq interaction are repulsive. The attractive interactions have stronger mu/T dependence than the repulsive interactions. 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.
QCD is expected to have a rich phase structure. It is empirically known to be difficult to access low temperature and nonzero chemical potential $mu$ regions in lattice QCD simulations. We address this issue in a lattice QCD with the use of a dimensi
onal reduction formula of the fermion determinant. We investigate spectral properties of a reduced matrix of the reduction formula. Lattice simulations with different lattice sizes show that the eigenvalues of the reduced matrix follow a scaling law for the temporal size $N_t$. The properties of the fermion determinant are examined using the reduction formula. We find that as a consequence of the $N_t$ scaling law, the fermion determinant becomes insensitive to $mu$ as $T$ decreases, and $mu$-independent at T=0 for $mu<m_pi/2$. The $N_t$ scaling law provides two types of the low temperature limit of the fermion determinant: (i) for low density and (ii) for high-density. The fermion determinant becomes real and the theory is free from the sign problem in both cases. In case of (ii), QCD approaches to a theory, where quarks interact only in spatial directions, and gluons interact via the ordinary Yang-Mills action. The partition function becomes exactly $Z_3$ invariant even in the presence of dynamical quarks because of the absence of the temporal interaction of quarks. The reduction formula is also applied to the canonical formalism and Lee-Yang zero theorem. We find characteristic temperature dependences of the canonical distribution and of Lee-Yang zero trajectory. Using an assumption on the canonical partition function, we discuss physical meaning of those temperature dependences and show that the change of the canonical distribution and Lee-Yang zero trajectory are related to the existence/absence of $mu$-induced phase transitions.
We report an implementation of a code for SU(3) matrix multiplication on Cell/B.E., which is a part of our project, Lattice Tool Kit on Cell/B.E.. On QS20, the speed of the matrix multiplication on SPE in single precision is 227GFLOPS and it becomes
20GFLOPS {this vaule was remeasured and corrcted.} together with data transfer from main memory by DNA transfer, which is 4.6% of the hardware peak speed (460GFLOPS), and is 7.4% of the theoretical peak speed of this calculation (268.77GFLOPS). We briefly describe our tuning procedure.
We report our recent studies on the finite density QCD obtained from lattice QCD simulation with clover-improved Wilson fermions of two flavor and RG-improved gauge action. We approach the subject from two paths, i.e., the imaginary and real chemical potentials.
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 fo
r $beta = 1.9, mu_I = 0.2618, kappa=0.1388$ on $8^3times 4$ lattice volume We also present a result of the matrix reduction formula for the Wilson fermion.
