Multistep Methods for Lattice QCD Simulations

TL;DR

This paper explores multistep geometric integrators as a potential solution to stability and accuracy issues in molecular dynamics simulations for lattice QCD, aiming to improve performance without high computational costs.

Contribution

It systematically reviews multistep methods and evaluates their suitability and advantages as molecular dynamics integrators in lattice QCD simulations.

Findings

Multistep methods can potentially enhance stability in lattice QCD simulations.

They may increase the order of accuracy without significant computational overhead.

The paper discusses the conditions under which multistep methods are effective.

Abstract

It is well-known that molecular dynamics integrators, which are used for lattice quantum chromodynamics (QCD), suffer from instabilities and possess a rather low order of the accuracy. Hence, it is highly desirable to construct a new class of geometric integrators, that overcomes these instability problems and increases the order of accuracy without increasing remarkably the computational costs. In this paper we consider for this purpose multistep methods and give an overview of known results to systematize important knowledge for such methods being the right choice for lattice QCD simulations. At the end we try to answer the question: can multistep method be used as molecular dynamic integrators and what might be the advantage of it.