arXiv subjects
Publications and source records attributed to Th. Lippert.
We present a report on the status of the GRAL project (Going Realistic And Light), which aims at simulating full QCD with two dynamical Wilson quarks below the vector meson decay threshold, m_ps/m_v < 0.5, making use of finite-size-scaling techniques.
The non-normality of Wilson-type lattice Dirac operators has important consequences - the application of the usual concepts from the textbook (hermitian) quantum mechanics should be reconsidered. This includes an appropriate definition of observables and the refinement of computational tools. We show that the truncated singular value expansion is the optimal approximation to the inverse operator D^{-1} and we prove that due to the gamma_5-hermiticity it is equivalent to gamma_5 times the truncated eigenmode expansion of the hermitian Wilson-Dirac operator.
We perform an eta' mass analysis based on a total of 1130 dynamical gauge field configurations, with 5 different quark mass values on lattices of size 16^3*32 (SESAM) and 24^3*40 (TkL) at beta = 5.6. We employ the stochastic estimator technique and spectral methods to deal with the disconnected piece of the flavour singlet correlation function. We demonstrate that very early plateau formation in the local eta' mass can be achieved by first ground state projecting the connected piece of its correlator.
As part of a systematic algorithm study, we present first results on a performance comparison between a multibosonic algorithm and the hybrid Monte Carlo algorithm as employed by the SESAM collaboration. The standard Wilson fermion action is used on 32*16^3 lattices at beta=5.5.
We demonstrate the utility of a spectral approximation to fermion loop operators using low-lying eigenmodes of the hermitian Dirac-Wilson matrix, Q. The investigation is based on a total of 400 full QCD vacuum configurations, with two degenerate flavors of dynamical Wilson fermions at beta =5.6, at two different sea quark masses. The spectral approach is highly competitive for accessing both topological charge and disconnected diagrams, on large lattices and small quark masses. We propose suitable partial summation techniques that provide sufficient saturation for estimating Tr Q^{-1}, which is related to the topological charge. In the effective mass plot of the eta' meson we achieved a consistent early plateau formation, by ground state projecting the connected piece of its propagator.
We consider the local chirality of near-zero eigenvectors from Wilson-Dirac and clover improved Wilson-Dirac lattice operators as proposed recently by Horváth et al. We studied finer lattices and repaired for the loss of orthogonality due to the non-normality of the Wilson-Dirac matrix. As a result we do see a clear double peak structure on lattices with resolutions higher than 0.1 fm. We found that the lattice artifacts can be considerably reduced by exploiting the biorthogonal system of left and right eigenvectors. We conclude that the dominance of instantons on topological charge fluctuations is not ruled out by local chirality measurements.
We describe results of a high-statistics finite size scaling analysis of 4d compact U(1) lattice gauge theory with Wilson action at the phase transition point. Using a multicanonical hybrid Monte Carlo algorithm we generate data samples with more than 150 tunneling events between the metastable states of the system, on lattice sizes up to 18^4. We performed a first analysis within the Borgs-Kotecky finite size scaling scheme. As a result, we report evidence for a first-order phase transition with a plaquette energy gap, G=0.02667(20), at a transition coupling, beta_T=1.011128(11).
We perform a lattice mass analysis in the flavour singlet pseudoscalar channel on the SESAM and TXL full QCD vacuum configurations, with 2 active flavours of dynamical Wilson fermions at beta = 5.6. At our inverse lattice spacing, a^-1 = 2.3 GeV, we retrieve by a chiral extrapolation to the physical light quark masses the value m_eta' = 3.7(+8)(-4) m_pi. A crude extrapolation from (N_f = 3) phenomenology would suggest m_eta' \approx 5.1 m_pi for N_f = 2 QCD. we verify that the mass gap between the singlet state eta' and the pi flavour triplt state is due to gauge configurations with non-trivial topology.
We present a study on the direct determination of the $η'$ mass on the full set of SESAM and T$χ$L QCD vacuum configurations with 2 active flavours of Wilson fermions, at $β= 5.6$. We observe a definite dependency of the two-loop correlator on the topological charge sector.
For lattice QCD with two sea quark flavours we compute the static quark antiquark potential V(R) in the regime where string breaking is expected. In order to increase statistics, we make full use of the lattice information by including all lattice vectors R to any possible lattice separation in the infrared regime. The corresponding paths between the lattice points are constructed by means of a generalized Bresenham algorithm as known from computer graphics. As a results we achieve a determination of the unquenched potential in the range .8 to 1.5 fm with hitherto unknown precision. Furthermore, we demonstrate some error reducing methods for the evaluation of the transition matrix element between two- and four-quark states.
It is shown that the 21264 Alpha processor can reach about 20% sustained efficiency for the inversion of the Wilson-Dirac operator. Since fast ethernet is not sufficient to get balancing between computation and communication on reasonable lattice- and system-sizes, an interconnection using Myrinet is discussed. We find a price/performance ratio comparable with state-of-the-art SIMD-systems for lattice QCD.
We demonstrate that substantial progress can be achieved in the study of the phase structure of 4-dimensional compact QED by a joint use of hybrid Monte Carlo and multicanonical algorithms, through an efficient parallel implementation. This is borne out by the observation of considerable speedup of tunnelling between the metastable states, close to the phase transition, on the Wilson line. Our approach leads to a general parallelization scheme for the efficient stochastic sampling of systems where (a part of) the Hamiltonian involves the total action or energy in each update step.
We estimate the QCD coupling constant from a lattice calculation of the bottomonium spectrum. The second order perturbative expansion of the plaquette expectation value is employed to determine alpha_S at a scale set by the 2S-1S and 1P-1S level splittings. The latter are computed in NRQCD in a dynamical gauge field background with two degenerate flavours of Wilson quarks at intermediate masses and extrapolated to the chiral limit. Combining the N_f=2 result with the quenched result at equal lattice spacing we extrapolate to the physical number of light flavours to find a value of alpha_{\bar MS}^{(5)}(m_Z) = 0.1118(17). The error quoted covers both statistical and systematic uncertainties in the scale determination. An additional 5% uncertainty comes from the choice of the underlying sea quark formulation and from truncation errors in perturbative expansions.
We present the final analysis of the light and strange hadron spectra from a full QCD lattice simulation with two degenerate dynamical sea quark flavours at $β= 5.6$ on a $16^3 \times 32$ lattice. Four sets of sea quark masses corresponding to the range $.69 \leq m_π/m_ρ\leq .83$ are investigated. For reference we also ran a quenched simulation at $β_{\sf eff} = 6.0$, which is the point of equal lattice spacing, $a_ρ^{-1}$. In the light sector, we find the chiral extrapolation to physical u- and d- masses to present a major source of uncertainty, comparable to the expected size of unquenching effects. From linear and quadratic fits we can estimate the errors on the hadron masses made from light quarks to be on a 15 % level prior to the continuum extrapolation. For the hadrons with strange valence quark content, the $N_F = 2$ approximation to QCD appears not to cure the well-known failure of quenched QCD to reproduce the physical $K-K^*$ splitting.
We demonstrate that substantial progress can be achieved in the study of the phase structure of 4-dimensional compact QED by a joint use of hybrid Monte Carlo and multicanonical algorithms, through an efficient parallel implementation. This is borne out by the observation of considerable speedup of tunnelling between the metastable states, close to the phase transition, on the Wilson line. We estimate that the creation of adequate samples (with order 100 flip-flops) becomes a matter of half a year's runtime at 2 Gflops sustained performance for lattices of size up to 24^4.
The investigation of the decorrelation efficiency of the HMC algorithm with respect to vacuum topology is a prerequisite for trustworthy full QCD simulations, in particular for the computation of topology sensitive quantities. We demonstrate that for mpi/mrho ratios <= 0.69 sufficient tunneling between the topological sectors can be achieved, for two flavours of dynamical Wilson fermions close to the scaling region beta=5.6. Our results are based on time series of length 5000 trajectories.
SSOR preconditioning of fermion matrix inversions which is parallelized using a locally-lexicographic lattice sub-division, has been shown to be very efficient for standard Wilson fermions. We demonstrate here the power of this method for the Sheikholeslami-Wohlert improved fermion action and for a renormalization group improved action incorporating couplings of the lattice fermion fields up to the diagonal in the unit hypercube.
We construct a locally-lexicographic SSOR preconditioner to accelerate the parallel iterative solution of linear systems of equations for two improved discretizations of lattice fermions: the Sheikholeslami-Wohlert scheme where a non-constant block-diagonal term is added to the Wilson fermion matrix and renormalization group improved actions which incorporate couplings beyond nearest neighbors of the lattice fermion fields. In case (i) we find the block llssor-scheme to be more effective by a factor about 2 than odd-even preconditioned solvers in terms of convergence rates, at beta=6.0. For type (ii) actions, we show that our preconditioner accelerates the iterative solution of a linear system of hypercube fermions by a factor of 3 to 4.