Alternative to Domain Wall Fermions

TL;DR

This paper proposes an alternative to domain wall fermions, providing bounds on the condition number and analyzing computational costs, suggesting a more efficient implementation of overlap Dirac operators.

Contribution

It introduces a new approach to domain wall fermions with bounds on condition numbers, and compares computational costs to existing methods.

Findings

Condition number of the new approach is similar to existing methods.

Implementation cost is comparable to direct overlap Dirac operator methods.

Memory usage can be optimized to be independent of approximation accuracy.

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.