Testing and tuning symplectic integrators for Hybrid Monte Carlo algorithm in lattice QCD

TL;DR

This paper evaluates a new 2nd order symplectic integrator for Hybrid Monte Carlo in lattice QCD, demonstrating it reduces energy errors and improves efficiency over the standard leapfrog method through parameter tuning.

Contribution

It introduces a refined parameter tuning of the new integrator, enhancing its efficiency and applicability in lattice QCD simulations compared to previous implementations.

Findings

The new integrator has 10 times smaller energy error than leapfrog.

It allows for three times larger step size, increasing efficiency by about 50%.

Optimal parameters depend on simulation specifics and differ slightly from previous estimates.

Abstract

We examine a new 2nd order integrator recently found by Omelyan et al. The integration error of the new integrator measured in the root mean square of the energy difference, $\bra\Delta H^2\ket^{1/2}$, is about 10 times smaller than that of the standard 2nd order leapfrog (2LF) integrator. As a result, the step size of the new integrator can be made about three times larger. Taking into account a factor 2 increase in cost, the new integrator is about 50% more efficient than the 2LF integrator. Integrating over positions first, then momenta, is slightly more advantageous than the reverse. Further parameter tuning is possible. We find that the optimal parameter for the new integrator is slightly different from the value obtained by Omelyan et al., and depends on the simulation parameters. This integrator could also be advantageous for the Trotter-Suzuki decomposition in Quantum Monte Carlo.