Reversibility Violation in the Hybrid Monte Carlo Algorithm

TL;DR

This paper examines how finite numerical precision causes reversibility violations in the Hybrid Monte Carlo algorithm, finding that physical observables are unaffected within certain bounds, which are independent of problem size and parameters.

Contribution

It provides an empirical condition for reversibility violations below which the HMC algorithm remains reliable, regardless of problem size and parameters.

Findings

Reversibility violations are inevitable with finite precision.

Physical observables show no significant deviation within certain violation bounds.

An upper bound for violations ensures reliable simulations, independent of problem size.

Abstract

We investigate reversibility violations in the Hybrid Monte Carlo algorithm. Those violations are inevitable when computers with finite numerical precision are being used. In SU(2) gauge theory, we study the dependence of observables on the size of the reversibility violations. While we cannot find any statistically significant deviation in observables related to the simulated physical model, algorithmic specific observables signal an upper bound for reversibility violations below which simulations appear unproblematic. This empirically derived condition is independent of problem size and parameter values, at least in the range of parameters studied here.