Adapted nested force-gradient integrators: the Schwinger model case

TL;DR

This paper introduces adapted nested force-gradient integrators for the HMC algorithm, demonstrating their efficiency in the Schwinger model by reducing computational costs compared to existing methods.

Contribution

The paper develops a new class of nested force-gradient integrators and shows their effectiveness in lattice gauge theory simulations.

Findings

Reduced computational costs in the Schwinger model

Analytical foundation for nested force-gradient methods

Improved efficiency over traditional integrators

Abstract

We study a novel class of numerical integrators, the adapted nested force-gradient schemes, used within the molecular dynamics step of the Hybrid Monte Carlo (HMC) algorithm. We test these methods in the Schwinger model on the lattice, a well known benchmark problem. We derive the analytical basis of nested force-gradient type methods and demonstrate the advantage of the proposed approach, namely reduced computational costs compared with other numerical integration schemes in HMC.