Improving dynamical lattice QCD simulations through integrator tuning using Poisson brackets and a force-gradient integrator

TL;DR

This paper introduces a new tuning method and a class of force-gradient integrators for molecular dynamics in lattice QCD simulations, aiming to improve efficiency by better conserving the Hamiltonian and reducing computational costs.

Contribution

It presents a novel integrator tuning approach and introduces force-gradient integrators that enhance the efficiency of lattice QCD simulations.

Findings

Force-gradient integrators reduce computational costs.

New tuning method improves Hamiltonian conservation.

Potential for more efficient large-scale gauge field simulations.

Abstract

We show how the integrators used for the molecular dynamics step of the Hybrid Monte Carlo algorithm can be further improved. These integrators not only approximately conserve some Hamiltonian $H$ but conserve exactly a nearby shadow Hamiltonian $\tilde{H}$. This property allows for a new tuning method of the molecular dynamics integrator and also allows for a new class of integrators (force-gradient integrators) which is expected to reduce significantly the computational cost of future large-scale gauge field ensemble generation.