Accelerated Overlap Fermions

Numerical evaluation of the overlap Dirac operator is difficult since it contains the sign function $\epsilon(H_w)$ 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.Comment: 15 pages, 6 figures; V2 contains major revision of the introduction and motivation sections. Conclusion and results unchanged v2.1: formatting chang

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, $\kappa$, 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.Comment: Lattice2002(chiral

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.Comment: 22 pages, 7 postscript figure

Scaling Behavior of the Landau Gauge Overlap Quark Propagator

The properties of the momentum space quark propagator in Landau gauge are examined for the overlap quark action in quenched lattice QCD. Numerical calculations are done on three lattices with different lattice spacings and similar physical volumes to explore the approach of the quark propagator towards the continuum limit. We have calculated the nonperturbative momentum-dependent wavefunction renormalization function $Z(p^2)$ and the nonperturbative mass function $M(p^2)$ for a variety of bare quark masses and extrapolate to the chiral limit. We find the behavior of $Z(p^2)$ and $M(p^2)$ are in good agreement for the two finer lattices in the chiral limit. The quark condensate is also calculated.Comment: 3 pages, Lattice2003(Chiral fermions

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.Comment: 5 pages, 8 figures, talk given by F.D.R. Bonnet at LHP 2001 workshop, Cairns, Australi