Tuning the Hybrid Monte Carlo algorithm using molecular dynamics forces’ variances

Preprint number: CP3-Origins-2018-1 DNRF90
Authors: Andrea Bussone (IFT Madrid), Vincent Drach (Plymouth Univ), Michele Della Morte (CP3-Origins), and Claudio Pica (CP3-Origins)

Within the HMC algorithm, we discuss how, by using the shadow Hamiltonian and
the Poisson brackets, one can achieve a simple factorization in the dependence of the
Hamiltonian violations upon either the algorithmic parameters or the parameters
specifying the integrator. We consider the simplest case of a second order (nested)
Omelyan intergrator and one level of Hasenbusch splitting of the determinant for
the simulations of a QCD-like theory (with gauge group SU(2)). Given the specic
choice of the integrator, the Poisson brackets reduce to the variances of the molecular
dynamics forces. We show how the factorization can be used to optimize in a very
economical and simple way both the algorithmic and the intergrator parameters
with good accuracy.