Polynomial Filtered HMC -- an algorithm for lattice QCD with dynamical quarks

TL;DR

This paper introduces Polynomial Filtered HMC, a new algorithm that uses polynomial approximations and a flexible multiple time-scale scheme to significantly reduce computational costs in lattice QCD simulations with dynamical quarks.

Contribution

It presents a novel generalisation of the nested leapfrog integrator, enabling more flexible time scale choices and improved efficiency in molecular dynamics for lattice QCD.

Findings

Achieves 3-5 times reduction in computational expense

Efficiency improves as quark mass decreases

Demonstrates effectiveness of polynomial filtering in HMC simulations

Abstract

Polynomial approximations to the inverse of the fermion matrix are used to filter the dynamics of the upper energy scales in HMC simulations. The use of a multiple time-scale integration scheme allows the filtered pseudofermions to be evolved using a coarse step size. We introduce a novel generalisation of the nested leapfrog which allows for far greater flexibility in the choice of time scales. We observe a reduction in the computational expense of the molecular dynamics integration of between 3--5 which improves as the quark mass decreases.