Alternative to Domain Wall Fermions

Abstract

An alternative to commonly used domain wall fermions is presented. Some rigorous bounds on the condition number of the associated linear problem are derived. On the basis of these bounds and some experimentation it is argued that domain wall fermions will in general be associated with a condition number that is of the same order of magnitude as the {\it product} of the condition number of the linear problem in the physical dimensions by the inverse bare quark mass. Thus, the computational cost of implementing true domain wall fermions using a single conjugate gradient algorithm is of the same order of magnitude as that of implementing the overlap Dirac operator directly using two nested conjugate gradient algorithms. At a cost of about a factor of two in operation count it is possible to make the memory usage of direct implementations of the overlap Dirac operator independent of the accuracy of the approximation to the sign function and of the same order as that of standard Wilson fermions.

7 pages, 1 figure, LaTeX, uses espcrc2, reference added

References in corpus (3)

• A practical implementation of the Overlap-Dirac operator
• Charge Deficiency, Charge Transport and Comparison of Dimensions
• Minimizing storage in implementations of the overlap lattice-Dirac operator

Cited by in corpus (10)

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• Filtered overlap: speedup, locality, kernel non-normality and Z_A~1
• Electric polarizability of hadrons with overlap fermions on multi-GPUs
• The eigSUMR inverter for overlap fermion
• Error Bounds for the Sign Function
• Lattice QCD and Flavour Physics
• Dynamical fermions in lattice quantum chromodynamics