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

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.

5 pages, 1 figure; minor changes

References in corpus (1)

• Asymptotics of Fixed Point Distributions for Inexact Monte Carlo Algorithms

Cited by in corpus (13)

• Two Nucleon Systems at $m_{\pi }\sim 450\mathrm{MeV}$ from Lattice QCD
• Lattice QCD for Cosmology
• Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond
• Slope and curvature of the hadron vacuum polarization at vanishing virtuality from lattice QCD
• Shadow Hamiltonians, Poisson Brackets, and Gauge Theories
• Diffusion of topological charge in lattice QCD simulations
• Lattice QCD static potentials of the meson-meson and tetraquark systems computed with both quenched and full QCD
• Status and challenges of simulations with dynamical fermions
• Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents
• Applying polynomial filtering to mass preconditioned Hybrid Monte Carlo
• Tuning the Hybrid Monte Carlo algorithm using molecular dynamics forces' variances
• A Unifying and Canonical Description of Measure-Preserving Diffusions
• Accuracy of Symmetric Partitioned Runge-Kutta Methods for Differential Equations on Lie-Groups