Instabilities in Molecular Dynamics Integrators used in Hybrid Monte Carlo Simulations

TL;DR

This paper identifies and analyzes an instability in the leapfrog integrator used in Hybrid Monte Carlo simulations of lattice QCD, demonstrating its effects in simple models and real simulations, and discussing implications for future research.

Contribution

It reveals a specific instability in the leapfrog algorithm within HMC for lattice QCD and explores its impact on simulations, providing insights for improving numerical stability.

Findings

Instability observed in simple harmonic oscillator model.

Instability manifested in lattice QCD simulations with Wilson-Clover fermions.

Discussion of implications for future lattice QCD simulations.

Abstract

We discuss an instability in the leapfrog integration algorithm, widely used in current Hybrid Monte Carlo (HMC) simulations of lattice QCD. We demonstrate the instability in the simple harmonic oscillator (SHO) system where it is manifest. We demonstrate the instability in HMC simulations of lattic QCD with dynamical Wilson-Clover fermions and discuss implications for future simulations of lattice QCD.