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Speeding up Lattice QCD simulations with clover-improved Wilson Fermions

M. Hasenbusch, K. Jansen

TL;DR

This work addresses the critical bottleneck of HMC simulations for dynamical Wilson fermions at light quark masses by introducing a modified pseudo-fermion action based on a two-factor decomposition of the fermion matrix. Two pseudo-fermion fields are used to sample the determinants of the two factors, with a tunable parameter $\rho$ designed to reduce the effective condition number and permit larger integration steps. Across $8^3\times24$ and $16^3\times24$ lattices at $\beta=5.2$ and $c_{sw}=1.76$, the approach yields speed-ups typically around 1.6–2.4×, with the Sexton-Weingarten integration scheme benefiting more than leap-frog. The method is compatible with existing even-odd preconditioning and offers a path toward improved scaling as the chiral limit is approached, with potential extensions to more factors or polynomial-based PHMC schemes.

Abstract

We apply a recent proposal to speed up the Hybrid-Monte-Carlo simulation of systems with dynamical fermions to two flavour QCD with clover-improvement. The basic idea of our proposal is to split the fermion matrix into two factors with a reduced condition number each. In the effective action, for both factors a pseudo-fermion field is introduced. For our smallest quark masses we see a speed-up of more than a factor of two compared with the standard algorithm.

Speeding up Lattice QCD simulations with clover-improved Wilson Fermions

TL;DR

This work addresses the critical bottleneck of HMC simulations for dynamical Wilson fermions at light quark masses by introducing a modified pseudo-fermion action based on a two-factor decomposition of the fermion matrix. Two pseudo-fermion fields are used to sample the determinants of the two factors, with a tunable parameter designed to reduce the effective condition number and permit larger integration steps. Across and lattices at and , the approach yields speed-ups typically around 1.6–2.4×, with the Sexton-Weingarten integration scheme benefiting more than leap-frog. The method is compatible with existing even-odd preconditioning and offers a path toward improved scaling as the chiral limit is approached, with potential extensions to more factors or polynomial-based PHMC schemes.

Abstract

We apply a recent proposal to speed up the Hybrid-Monte-Carlo simulation of systems with dynamical fermions to two flavour QCD with clover-improvement. The basic idea of our proposal is to split the fermion matrix into two factors with a reduced condition number each. In the effective action, for both factors a pseudo-fermion field is introduced. For our smallest quark masses we see a speed-up of more than a factor of two compared with the standard algorithm.

Paper Structure

This paper contains 18 sections, 57 equations, 2 figures, 7 tables.

Table of Contents

  1. Introduction
  2. The modified pseudo-fermion action
  3. The model
  4. The modified pseudo-fermion action
  5. The Hybrid-Monte-Carlo Algorithm
  6. Heat-bath of the pseudo-fermion fields
  7. The variation of the pseudo-fermion action
  8. Integration schemes
  9. The Numerical Study
  10. Details of the implementation
  11. The action $S_F$
  12. The action $\tilde{S}_F$
  13. Analysing the Performance of the Algorithm
  14. Simulation results
  15. Simulations of the $8^3 \times 24$ lattice
  16. ...and 3 more sections

Figures (2)

  • Figure 1: Results for the acceptance rate of the leap-frog scheme (circle) and the Sexton-Weingarten improved scheme (triangle) as function of the parameter $\rho$. The dashed and the dotted lines should only guide the eye. For the leap-frog scheme, we have fixed the step-size to $\delta \tau=0.02$ and for the Sexton-Weingarten improved scheme to $\delta \tau=0.05$. The simulations are performed on a $8^3\times 24$ lattice at $\beta=5.2$, $c_{sw}=1.76$ and $\kappa=0.137$. The pseudo-fermion action $S_F$ of eq. (\ref{['orginal']}) is used.
  • Figure 2: Performance results in terms of the total number of iterations $N^{total}$ in the BiCGstab solver as a function of $\rho$. We denote by (L) the leap frog and by (S) the improved integration scheme.