A Novel Multiple-Time Scale Integrator for the Hybrid Monte Carlo Algorithm

TL;DR

This paper introduces a flexible multiple-time scale integrator for Hybrid Monte Carlo simulations, overcoming limitations of the traditional nested leapfrog method by allowing more adaptable time scale choices.

Contribution

A new integrator generalization that permits arbitrary multiple relationships between time scales, enhancing simulation flexibility.

Findings

Improved flexibility in choosing time scales.

Maintains accuracy with more adaptable step size selection.

Potential for more efficient Hybrid Monte Carlo simulations.

Abstract

Hybrid Monte Carlo simulations that implement the fermion action using multiple terms are commonly used. By the nature of their formulation they involve multiple integration time scales in the evolution of the system through simulation time. These different scales are usually dealt with by the Sexton-Weingarten nested leapfrog integrator. In this scheme the choice of time scales is somewhat restricted as each time step must be an exact multiple of the next smallest scale in the sequence. A novel generalisation of the nested leapfrog integrator is introduced which allows for far greater flexibility in the choice of time scales, as each scale now must only be an exact multiple of the smallest step size.