Accelerated Overlap Fermions

TL;DR

This paper explores methods to accelerate the numerical evaluation of the overlap Dirac operator by modifying the Wilson-Dirac operator, achieving a twofold speedup through the use of a FLIC action.

Contribution

It demonstrates that incorporating the clover term and link smearing in the Wilson-Dirac operator significantly speeds up overlap computations.

Findings

Achieved a twofold speedup in overlap operator evaluation.

Including the clover term improves the continuum-like properties of the kernel.

Smearing link variables reduces eigenvalue smallness issues.

Abstract

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.