arXiv subjects
Publications and source records attributed to K. Schilling.
We report new results from our finite size scaling analysis of 4d compact pure U(1) gauge theory with Wilson action. Investigating several cumulants of the plaquette energy within the Borgs-Kotecky finite size scaling scheme we find strong evidence for a first-order phase transition and present a high precision value for the critical coupling in the thermodynamic limit.
We present new results from our ongoing study of flavor singlet pseudoscalar mesons in QCD. Our approach is based on (a) performing truncated eigenmode expansions for the hairpin diagram and (b) incorporating the ground state contribution for the connected meson propagator. First, we explain how the computations can be substantially improved by even-odd preconditioning. We extend previous results on early mass plateauing in the eta' channel of two-flavor full QCD with degenerate sea and valence quarks to the partially quenched situation. We find that early mass plateau formation persists in the partially quenched situation.
Moments of the quark density, helicity, and transversity distributions are calculated in unquenched lattice QCD. Calculations of proton matrix elements of operators corresponding to these moments through the operator product expansion have been performed on $16^3 \times 32$ lattices for Wilson fermions at $β= 5.6$ using configurations from the SESAM collaboration and at $β= 5.5$ using configurations from SCRI. One-loop perturbative renormalization corrections are included. At quark masses accessible in present calculations, there is no statistically significant difference between quenched and full QCD results, indicating that the contributions of quark-antiquark excitations from the Dirac Sea are small. Close agreement between calculations with cooled configurations containing essentially only instantons and the full gluon configurations indicates that quark zero modes associated with instantons play a dominant role. Naive linear extrapolation of the full QCD calculation to the physical pion mass yields results inconsistent with experiment. Extrapolation to the chiral limit including the physics of the pion cloud can resolve this discrepancy and the requirements for a definitive chiral extrapolation are described.
The numerical and computational aspects of the overlap formalism in lattice quantum chromodynamics are extremely demanding due to a matrix-vector product that involves the sign function of the hermitian Wilson matrix. In this paper we investigate several methods to compute the product of the matrix sign-function with a vector, in particular Lanczos based methods and partial fraction expansion methods. Our goal is two-fold: we give realistic comparisons between known methods together with novel approaches and we present error bounds which allow to guarantee a given accuracy when terminating the Lanczos method and the multishift-CG solver, applied within the partial fraction expansion methods.
We apply spectral methods to compute the OZI-rule suppressed loop-loop correlators in the pseudoscalar meson flavour singlet channel. Using SESAM configurations (obtained with two degenerate sea quark flavours on 16x16x16x32 lattices at beta = 5.6 with standard Wilson action), we find for the first time clear evidence for mass plateau formation in the eta' channel of this theory. As a consequence, we observe a clear signal of a mass gap persistent under chiral extrapolation. This sets the stage for a more realistic two-channel approach, where partially quenched strange quarks would be included, in addition to u, d sea quarks.
In order to construct improved overlap fermions, we start from a short ranged approximate Ginsparg-Wilson fermion and insert it into the overlap formula. We show that its polynomial evaluation is accelerated considerably compared to the standard Neuberger fermion. In addition the degree of locality is strongly improved.
Improvements of various methods to compute the sign function of the hermitian Wilson-Dirac matrix within the overlap operator are presented. An optimal partial fraction expansion (PFE) based on a theorem of Zolotarev is given. Benchmarks show that this PFE together with removal of converged systems within a multi-shift CG appears to approximate the sign function times a vector most efficiently. A posteriori error bounds are given.
We present new data on the mass of the light and strange quarks from SESAM/T$χ$L. The results were obtained on lattice-volumes of $16^3\times 32$ and $24^3\times 40$ points, with the possibility to investigate finite-size effects. Since the SESAM/T$χ$L ensembles at $β=5.6$ have been complemented by configurations with $β=5.5$, moreover, we are now able to attempt the continuum extrapolation (CE) of the quark masses with standard Wilson fermions.
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 describe an explicit construction of approximate Ginsparg-Wilson fermions for QCD. We use ingredients of perfect action origin, and further elements. The spectrum of the lattice Dirac operator reveals the quality of the approximation. We focus on beta =6 for optimisation. Such fermions are intended to be inserted into the overlap formula. Hence we also test the speed of convergence under polynomial evaluation of the overlap formula.
Moments of the quark density distribution, moments of the quark helicity distribution, and the tensor charge are calculated in full QCD. Calculations of matrix elements of operators from the operator product expansion have been performed on $16^3 \times 32$ lattices for Wilson fermions at $β= 5.6$ using configurations from the SESAM collaboration and at $β= 5.5$ using configurations from SCRI. One-loop perturbative renormalization corrections are included. Selected results are compared with corresponding quenched calculations and with calculations using cooled configurations.
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.