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Lattice QCD on Small Computers

M. Alford, W. Dimm, G. P. Lepage, G. Hockney, P. B. Mackenzie

TL;DR

This paper tackles the high computational cost of lattice QCD by employing perturbatively-improved, tadpole-improved actions that remove leading lattice artifacts, enabling accurate simulations on coarse lattices up to $a \approx 0.4$ fm. The authors construct an improved gluon action with plaquette, rectangle, and parallelogram terms and determine their couplings via tadpole-improved perturbation theory, achieving near-continuum results for the static potential and the charmonium spectrum on desktop hardware. They demonstrate 10^3–10^6x speedups over unimproved calculations and show that key observables are largely independent of lattice spacing within a few percent. The findings imply that nonperturbative QCD physics can be explored more broadly and cost-effectively, with potential future refinements from nonperturbative coefficient determinations or Monte Carlo renormalization group techniques.

Abstract

We demonstrate that lattice QCD calculations can be made $10^3$--$10^6$ times faster by using very coarse lattices. To obtain accurate results, we replace the standard lattice actions by perturbatively-improved actions with tadpole-improved correction terms that remove the leading errors due to the lattice. To illustrate the power of this approach, we calculate the static-quark potential, and the charmonium spectrum and wavefunctions using a desktop computer. We obtain accurate results that are independent of the lattice spacing and agree well with experiment.

Lattice QCD on Small Computers

TL;DR

This paper tackles the high computational cost of lattice QCD by employing perturbatively-improved, tadpole-improved actions that remove leading lattice artifacts, enabling accurate simulations on coarse lattices up to fm. The authors construct an improved gluon action with plaquette, rectangle, and parallelogram terms and determine their couplings via tadpole-improved perturbation theory, achieving near-continuum results for the static potential and the charmonium spectrum on desktop hardware. They demonstrate 10^3–10^6x speedups over unimproved calculations and show that key observables are largely independent of lattice spacing within a few percent. The findings imply that nonperturbative QCD physics can be explored more broadly and cost-effectively, with potential future refinements from nonperturbative coefficient determinations or Monte Carlo renormalization group techniques.

Abstract

We demonstrate that lattice QCD calculations can be made -- times faster by using very coarse lattices. To obtain accurate results, we replace the standard lattice actions by perturbatively-improved actions with tadpole-improved correction terms that remove the leading errors due to the lattice. To illustrate the power of this approach, we calculate the static-quark potential, and the charmonium spectrum and wavefunctions using a desktop computer. We obtain accurate results that are independent of the lattice spacing and agree well with experiment.

Paper Structure

This paper contains 4 sections, 10 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. The Improved Action
  3. Monte-Carlo Results
  4. Conclusions

Figures (3)

  • Figure 1: Static-quark potential computed on $6^4$ lattices with $a\approx 0.4$ fm using the $\beta=4.5$ Wilson action and the improved action with $\beta_{\rm pl} = 6.8$.
  • Figure 2: $S$, $P$, and $D$ states of charmonium computed on lattices with: $a=0.40$ fm (improved action, $\beta_{\rm pl}=6.8$); $a=0.33$ fm (improved action, $\beta_{\rm pl}=7.1$); $a=0.24$ fm (improved action, $\beta_{\rm pl}=7.4$); and $a=0.17$ fm (Wilson action, $\beta=5.7$, from [6]). The dashed lines indicate the true masses.
  • Figure 3: The radial wavefunctions for the $1S$ and $1P$ charmonium computed using improved actions and two different lattice spacings. Wavefunctions from a continuum quark model are also shown. Statistical errors are negligible for the $1S$ wavefunction.