arXiv subjects

A. G. Williams

Publications and source records attributed to A. G. Williams.

At least 91 records · Page 5Linked to original sources

arXiv2002

FLIC Overlap Fermions

The action of the overlap-Dirac operator on a vector is typically implemented indirectly through a multi-shift conjugate gradient solver. The compute-time required depends upon the condition number, $κ$, of the matrix that is used as the overlap kernel. While the Wilson action is typically used as the overlap kernel, the FLIC (Fat Link Irrelevant Clover) action has an improved condition number and provides up to a factor of two speedup in evaluating the overlap action. We summarize recent progress on the use of FLIC overlap fermions.

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arXiv2002

FLIC-Overlap Fermions and Topology

APE smearing the links in the irrelevant operators of clover fermions (Fat-Link Irrelevant Clover (FLIC) fermions) provides significant improvement in the condition number of the Hermitian-Dirac operator and gives rise to a factor of two savings in computing the overlap operator. This report investigates the effects of using a highly-improved definition of the lattice field-strength tensor F_mu_nu in the fermion action, made possible through the use of APE-smeared fat links in the construction of the irrelevant operators. Spurious double-zero crossings in the spectral flow of the Hermitian-Wilson Dirac operator associated with lattice artifacts at the scale of the lattice spacing are removed with FLIC fermions composed with an O(a^4)-improved lattice field strength tensor. Hence, FLIC-Overlap fermions provide an additional benefit to the overlap formalism: a correct realization of topology in the fermion sector on the lattice.

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arXiv2002

Modelling the quark propagator

The quark propagator is at the core of lattice hadron spectrum calculations as well as studies in other nonperturbative schemes. We investigate the quark propagator with an improved staggered action (Asqtad) and an improved gluon action, which provides good quality data down to small quark masses. This is used to construct ansätze suitable for model hadron calculations as well as adding to our intuitive understanding of QCD.

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arXiv2002

Towards the Continuum Limit of the Overlap Quark Propagator in Landau Gauge

The properties of the momentum space quark propagator in Landau gauge are examined for the overlap quark action in quenched lattice QCD. Numerical calculations were done on two lattices with different lattice spacing $a$ and similar physical volumes to explore the quark propagator in the continuum limit. We have calculated the nonperturbative wavefunction renormalization function $Z(p)$ and the nonperturbative mass function $M(p)$ for a variety of bare quark masses and perform a simple linear extrapolation to the chiral limit. We find the behaviour of $Z(p)$ and $M(p)$ in the chiral limit are in good agreement between the two lattices.

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arXiv2002

Gluon Propagator on Coarse Lattices in Laplacian Gauges

The Laplacian gauge is a nonperturbative gauge fixing that reduces to Landau gauge in the asymptotic limit. Like Landau gauge, it respects Lorentz invariance, but it is free of Gribov copies; the gauge fixing is unambiguous. In this paper we study the infrared behavior of the lattice gluon propagator in Laplacian gauge by using a variety of lattices with spacings from $a = 0.125$ to 0.35 fm, to explore finite volume and discretization effects. Three different implementations of the Laplacian gauge are defined and compared. The Laplacian gauge propagator has already been claimed to be insensitive to finite volume effects and this is tested on lattices with large volumes.

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arXiv2002

Highly-improved lattice field-strength tensor

We derive an O(a^4)-improved lattice version of the continuum field-strength tensor. Discretization errors are reduced via the combination of several clover terms of various sizes, complemented by tadpole improvement. The resulting improved field-strength tensor is used to construct O(a^4)-improved topological charge and action operators. We compare the values attained by these operators as we cool several configurations to self-duality with a previously defined highly-improved action and assess the relative scale of the remaining discretization errors.

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arXiv2002

Accelerated Overlap Fermions

Numerical evaluation of the overlap Dirac operator is difficult since it contains the sign function $ε(H_w)$ of the Hermitian Wilson-Dirac operator $H_w$ with a negative mass term. The problems are due to $H_w$ having very small eigenvalues on the equilibrium background configurations generated in current day Monte Carlo simulations. Since these are a consequence of the lattice discretisation and do not occur in the continuum version of the operator, we investigate in this paper to what extent the numerical evaluation of the overlap can be accelerated by making the Wilson-Dirac operator more continuum-like. Specifically, we study the effect of including the clover term in the Wilson-Dirac operator and smearing the link variables in the irrelevant terms. In doing so, we have obtained a factor of two speedup by moving from the Wilson action to a FLIC (Fat Link Irrelevant Clover) action as the overlap kernel.

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arXiv2002

Lattice quark propagator with staggered quarks in Landau and Laplacian gauges

We report on the lattice quark propagator using standard and improved Staggered quark actions, with the standard, Wilson gauge action. The standard Kogut-Susskind action has errors of \oa{2} while the ``Asqtad'' action has \oa{4}, \oag{2}{2} errors. The quark propagator is interesting for studying the phenomenon of dynamical chiral symmetry breaking and as a test-bed for improvement. Gauge dependent quantities from lattice simulations may be affected by Gribov copies. We explore this by studying the quark propagator in both Landau and Laplacian gauges. Landau and Laplacian gauges are found to produce very similar results for the quark propagator.

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arXiv2002

QCD, Gauge Fixing, and the Gribov Problem

The standard techniques of gauge-fixing, such as covariant gauge fixing, are entirely adequate for the purposes of studies of perturbative QCD. However, they fail in the nonperturbative regime due to the presence of Gribov copies. These copies arise because standard local gauge fixing methods do not completely fix the gauge. Known Gribov-copy-free gauges, such as Laplacian gauge, are manifestly non-local. These issues are examined and the implications of non-local gauge-fixing for ghost fields, BRST invariance, and the proof of renormalizability of QCD are considered.

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arXiv2002

Quark propagator in a covariant gauge

Using mean--field improved gauge field configurations, we compare the results obtained for the quark propagator from Wilson fermions and Overlap fermions on a $\3$ lattice at a spacing of $a=0.125(2)$ fm.

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arXiv2002

Numerical study of lattice index theorem usingimproved cooling and overlap fermions

We investigate topological charge and the index theorem on finite lattices numerically. Using mean field improved gauge field configurations we calculate the topological charge Q using the gluon field definition with ${\cal O}(a^4)$-improved cooling and an ${\cal O}(a^4)$-improved field strength tensor $F_{μν}$. We also calculate the index of the massless overlap fermion operator by directly measuring the differences of the numbers of zero modes with left- and right--handed chiralities. For sufficiently smooth field configurations we find that the gluon field definition of the topological charge is integer to better than 1% and furthermore that this agrees with the index of the overlap Dirac operator, i.e., the Atiyah-Singer index theorem is satisfied. This establishes a benchmark for reliability when calculating lattice quantities which are very sensitive to topology.

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arXiv2002

Hadron Masses From Novel Fat-Link Fermion Actions

The hadron mass spectrum is calculated in lattice QCD using a novel fat-link clover fermion action in which only the irrelevant operators in the fermion action are constructed using smeared links. The simulations are performed on a 16^3 x 32 lattice with a lattice spacing of a=0.125 fm. We compare actions with n=4 and 12 smearing sweeps with a smearing fraction of 0.7. The n=4 Fat-Link Irrelevant Clover (FLIC) action provides scaling which is superior to mean-field improvement, and offers advantages over nonperturbative 0(a) improvement, including a reduced exceptional configuration problem.

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arXiv2002

Baryon resonances from a novel fat-link fermion action

We present first results for masses of positive and negative parity excited baryons in lattice QCD using an O(a^2) improved gluon action and a Fat Link Irrelevant Clover (FLIC) fermion action in which only the irrelevant operators are constructed with fat links. The results are in agreement with earlier calculations of N^* resonances using improved actions and exhibit a clear mass splitting between the nucleon and its chiral partner, even for the Wilson fermion action. The results also indicate a splitting between the lowest J^P = 1/2^- states for the two standard nucleon interpolating fields.

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arXiv2002

Novel fat-link fermion actions

The hadron mass spectrum is calculated in lattice QCD using a novel fat-link clover fermion action in which only the irrelevant operators of the fermion action are constructed using smeared links. The simulations are performed on a 16^3 X 32 lattice with a lattice spacing of a=0.125 fm. We compare actions with n=4 and 12 smearing sweeps with a smearing fraction of 0.7. The n=4 Fat Link Irrelevant Clover (FLIC) action provides scaling which is superior to mean-field improvement, and offers advantages over nonperturbative O(a) improvement.

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arXiv2001

Improving the low-lying spectrum of the overlap kernel

The action of the overlap-Dirac operator on a vector is typically implemented in directly through a multi-shift conjugate gradient solver. The compute-time this takes to evaluate depends upon the condition number $κ$ of the matrix that is used as the overlap kernel. We examine the low-lying spectra of various candidate kernels in an effort to optimise $κ$, thereby speeding up the overlap evaluation.

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arXiv2001

Cooling for instantons and the Wrath of Nahm

The dynamics of instantons and anti-instantons in lattice QCD can be studied by analysing the action and topological charge of configurations as they approach a self-dual or anti-self-dual state, i.e. a state in which S/S_0=|Q|. We use cooling to reveal the semi-classical structure of the configurations we study. Improved actions which eliminate discretization errors up to and including O(a^4) are used to stabilise instantons as we cool for several thousand sweeps. An analogously improved lattice version of the continuum field-strength tensor is used to construct a topological charge free from O(a^4) discretization errors. Values of the action and topological charge obtained with these improved operators approach mutually-consistent integer values to within a few parts in 10^4 after several hundred cooling sweeps. Analysis of configurations with |Q| \approx 1 and |Q| \approx 2 supports the hypothesis that a self-dual |Q|=1 configuration cannot exist on the 4-torus.

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arXiv2001

Quark propagator from an improved staggered action in Laplacian and Landau gauges

Studies of gauge dependent quantities are afflicted with Gribov copies, but Laplacian gauge fixing provides one possible solution to this problem. We present results for the lattice quark propagator in both Landau and Laplacian gauges using standard and improved staggered quark actions. The standard Kogut-Susskind action has errors of \oa{2} while the improved ``Asqtad'' action has \oa{4}, \oag{2}{2} errors and this improvement is seen in the quark propagator. We demonstrate the application of tree-level corrections to these actions and see that Landau and Laplacian gauges produce very similar results. In addition, we test an ansatz for the quark mass function, with promising results. In the chiral limit, the infrared quark mass, $M(q^2 = 0)$ is found to be $260\pm 20$ MeV.

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arXiv2001

Lattice Quark Propagator in Landau and Laplacian Gauges

We present results for the lattice quark propagator in both Landau and Laplacian gauges using standard and improved staggered quark actions. The standard Kogut-Susskind action has errors of \oa{2} while the improved ``Asqtad'' action has \oa{4}, \oag{2}{2} errors. This improvement is seen in the quark propagator. We demonstrate the application of tree-level corrections to these actions and see that Landau and Laplacian gauges produce very similar results.

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