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The RHMC Algorithm for 2 Flavours of Dynamical Staggered Fermions

M. A. Clark, A. D. Kennedy

TL;DR

The paper addresses two-flavour dynamical staggered fermion simulations and the algorithmic errors intrinsic to not fully exact methods. It advocates the Rational Hybrid Monte Carlo (RHMC) approach, which uses Chebyshev rational approximations to fractional powers of the fermion kernel and a multishift solver to implement an exact HMC-like procedure without MD stepsize errors, or with a controlled Metropolis test. It also discusses noisy variants (RHMCN) and compares RHMC to the traditional $R$ algorithm, finding RHMC nearly as costly but significantly more exact, with RHMCN incurring higher costs. The work demonstrates that RHMC extends exact simulation to arbitrary flavour numbers and offers practical advantages over the $R$ algorithm for lattice QCD with staggered fermions.

Abstract

We describe an implementation of the Rational Hybrid Monte Carlo (RHMC) algorithm for dynamical computations with two flavours of staggered quarks. We discuss several variants of the method, the performance and possible sources of error for each of them, and we compare the performance and results to the inexact R algorithm.

The RHMC Algorithm for 2 Flavours of Dynamical Staggered Fermions

TL;DR

The paper addresses two-flavour dynamical staggered fermion simulations and the algorithmic errors intrinsic to not fully exact methods. It advocates the Rational Hybrid Monte Carlo (RHMC) approach, which uses Chebyshev rational approximations to fractional powers of the fermion kernel and a multishift solver to implement an exact HMC-like procedure without MD stepsize errors, or with a controlled Metropolis test. It also discusses noisy variants (RHMCN) and compares RHMC to the traditional algorithm, finding RHMC nearly as costly but significantly more exact, with RHMCN incurring higher costs. The work demonstrates that RHMC extends exact simulation to arbitrary flavour numbers and offers practical advantages over the algorithm for lattice QCD with staggered fermions.

Abstract

We describe an implementation of the Rational Hybrid Monte Carlo (RHMC) algorithm for dynamical computations with two flavours of staggered quarks. We discuss several variants of the method, the performance and possible sources of error for each of them, and we compare the performance and results to the inexact R algorithm.

Paper Structure

This paper contains 8 sections, 5 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Two Flavour Algorithms
  3. The $R$ algorithm
  4. Rational Hybrid Molecular Dynamics
  5. Rational Hybrid Monte Carlo
  6. Noisy Rational Hybrid Monte Carlo
  7. Comparison of RHMC and $R$
  8. Conclusion

Figures (1)

  • Figure 1: Comparison of minimax errors for optimal rational and polynomial approximating functions to $x^{-1/2}$ over the range [0.00003,1] (corresponding to staggered mass parameter $m=0.025$) as a function of approximation degree.