Single flavour optimisations to Hybrid Monte Carlo

TL;DR

This paper introduces filtering techniques and a new tuning method to improve the efficiency of single-flavour Hybrid Monte Carlo simulations in lattice QCD, reducing computational costs.

Contribution

It presents two filtering methods for RHMC in single-flavour simulations and a novel step-size tuning technique, enhancing computational efficiency.

Findings

Filtering methods significantly reduce simulation costs.

The tuning technique improves step-size selection.

Methods are validated on different lattice volumes.

Abstract

It has become increasingly important to include one or more individual flavours of dynamical fermion in lattice QCD simulations. This is due in part to the advent of QCD+QED calculations, where isospin symmetry breaking means that the up, down, and strange quarks must be treated separately. These single-flavour pseudofermions are typically implemented as rational approximations to the inverse of the fermion matrix, using the technique known as Rational Hybrid Monte Carlo (RHMC). Over the years, a wide range of methods have been developed for accelerating simulations of two degenerate flavours of pseudofermion, while there are comparatively fewer such techniques for single-flavour pseudofermions. Here, we investigate two different filtering methods that can be applied to RHMC for simulating single-flavour pseudofermions, namely polynomial filtering (PF-RHMC), and filtering via truncations of the ordered product (tRHMC). A novel integration step-size tuning technique based on the characteristic scale is also introduced. Studies are performed on two different lattice volumes, demonstrating that one can achieve significant reductions in the computational cost of single-flavour simulations with these filtering techniques.