The lattice QCD simulation with the lattice chiral symmetry is very attractive, however, it is difficult to maintain the symmetry at a modest numerical computation cost. A candidate to reduce the computational cost during the configuration generation
with the HMC algorithm is to relax the requirement of the chiral symmetry and to use the reweighing method recovering the symmetry at the measurement phase. In this talk, we presented the reweighing method to restore the chiral symmetry of the truncated overlap fermion operator. In order to avoid the large discrepancy between the truncated overlap operator and the exact overlap operator, we split the reweighting factor into several steps gradually increasing the order of truncation. We investigated the truncation dependence of the reweighting factor on a set of quenched $8^3times 32$ lattice configurations generated with the DBW2 gauge action. We found that a large fluctuation on the reweighting factor between a high-order truncated overlap operator and the exact overlap operator on a couple of configurations. The origin of the large fluctuation seems to be due to a small eigenvalue of the overlap kernel on these configurations.
Hattori-Itakura have recently derived the full Landau-level summation form for the photon vacuum polarization tensor in constant external magnetic fields at the one-loop level. The Landau-level summation form is essential when the photon momentum exc
eeds the threshold of the pair creation of charged particles in a magnetic field stronger than the squared mass of the charged particle. The tensor has three different form factors depending on the tensor direction with respect to the external magnetic field. The renormalization is nontrivial because these form factors are expressed in terms of double or triple summation forms. We give a numerical UV subtraction method which can be applied to numerically evaluate the form factors in constant external magnetic fields. We numerically investigate the photon vacuum polarization tensor in the form of the Landau-level summation and estimate the systematic errors coming from truncation of the Landau-level summation in a parameter region realized in heavy ion collision experiments. We find that the error is practically controllable at an $O(10^{-2})$ level for electrons and muons in strong magnetic fields expected in heavy ion collisions in the experimentally feasible kinematic parameter regions.
We study the algorithmic optimization and performance tuning of the Lattice QCD clover-fermion solver for the K computer. We implement the Luschers SAP preconditioner with sub-blocking in which the lattice block in a node is further divided to severa
l sub-blocks to extract enough parallelism for the 8-core CPU SPARC64$^{mathrm{TM}}$ VIIIfx of the K computer. To achieve a better convergence property we use the symmetric successive over-relaxation (SSOR) iteration with {it locally-lexicographical} ordering for the sub-blocks in obtaining the block inverse. The SAP preconditioner is included in the single precision BiCGStab solver of the nested BiCGStab solver. The single precision part of the computational kernel are solely written with the SIMD oriented intrinsics to achieve the best performance of the SPARC on the K computer. We benchmark the single precision BiCGStab solver on the three lattice sizes: $12^3times 24$, $24^3times 48$ and $48^3times 96$, with fixing the local lattice size in a node at $6^3times 12$. We observe an ideal weak-scaling performance from 16 nodes to 4096 nodes. The performance of a computational kernel exceeds 50% efficiency, and the single precision BiCGstab has $sim26% susutained efficiency.
We accelerate many-flavor lattice QCD simulations using multiple GPUs. Multiple pseudo-fermion fields are introduced additively and independently for each flavor in the many-flavor HMC algorithm. Using the independence of each pseudo-fermion field an
d the blocking technique for the quark solver, we can assign the solver task to each GPU card. In this report we present the blocking technique for the many-flavor dynamical QCD simulations. We investigate the effect of the blocking and the acceleration with the multiple GPUs for the Schr{o}dinger functional simulations with Wilson SU(3) plaquette gauge action and $N_f=10$ Wilson fermions. Five pseudo-fermion fields are introduced and the quark solver task is distributed in the ratio of 2:3 to two GPUs. We expect a 40% timing reduction from the single GPU case and have observed a 34% timing reduction in the test simulations.
