Iterative methods for overlap and twisted mass fermions

TL;DR

This paper compares iterative solvers for fermion propagators in lattice QCD, showing that overlap fermions are significantly more computationally expensive than twisted mass fermions across various algorithms and parameters.

Contribution

It provides a detailed comparison of iterative methods for overlap and twisted mass fermions, highlighting their computational costs and efficiencies in lattice QCD.

Findings

Overlap fermions are 30-120 times more expensive than twisted mass fermions.

Adaptive precision and low mode preconditioning improve overlap fermion computations.

Even/odd preconditioning benefits twisted mass fermion calculations.

Abstract

We present a comparison of a number of iterative solvers of linear systems of equations for obtaining the fermion propagator in lattice QCD. In particular, we consider chirally invariant overlap and chirally improved Wilson (maximally) twisted mass fermions. The comparison of both formulations of lattice QCD is performed at four fixed values of the pion mass between 230MeV and 720MeV. For overlap fermions we address adaptive precision and low mode preconditioning while for twisted mass fermions we discuss even/odd preconditioning. Taking the best available algorithms in each case we find that calculations with the overlap operator are by a factor of 30-120 more expensive than with the twisted mass operator.