We study the phase structure of QCD in the $T-mu$ plane using a histogram method and the reweighting technique by performing phase quenched simulations of two-flavor QCD with RG-improved gauge action and O($a$) improved Wilson quark action. Taking th
e effects of the complex phase of the quark determinant using the cumulant expansion method, we calculate the probability distribution function of plaquette and phase-quenched determinant as a function of $T$ and $mu$. We discuss the order of the QCD phase transition consulting the shape of the probability distribution function.
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 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.
