Kramers equation algorithm for simulations of QCD with two flavors of Wilson fermions and gauge group SU(2)

TL;DR

This paper compares the Kramers equation and Hybrid Monte Carlo algorithms for simulating two-flavor Wilson fermions in SU(2) QCD, analyzing their performance and dynamical properties on various lattice sizes.

Contribution

It introduces the Kramers equation algorithm as an alternative to HMC for lattice QCD simulations and evaluates its efficiency and dynamical behavior.

Findings

Kramers algorithm performs comparably to HMC in simulations.

Classical equations of motion exhibit non-reversibility and chaotic behavior.

Both algorithms show similar efficiency across tested lattice sizes.

Abstract

We compare the Hybrid Monte Carlo (HMC) and the Kramers equation algorithms for simulations of QCD with two flavors of dynamical Wilson fermions and gauge group $SU(2)$. The results for the performance of both algorithms are obtained on $6^312$, $12^4$ and $16^4$ lattices at a pion to $\rho$ meson mass ratio of $m_\pi/m_\rho \approx 0.9$. We find that the Kramers equation algorithm gives an equally good performance as the HMC algorithm. We demonstrate that the classical equations of motion used in these algorithms lack reversibility in practical simulations and behave like those of a chaotic dynamical system with a Liapunov exponent $\nu \approx 0.75$.