QCD on the 16-cell honeycomb

TL;DR

The paper explores discretizing QCD on the vertex set of the 4D 16-cell honeycomb to enhance symmetry and suppress cut-off artifacts compared with the standard cubic lattice. The authors develop a triangle-based gauge action and implement Wilson-Dirac fermions with clover improvement and stout smearing in quenched QCD, using gradient flow and the $t_0$ scale to study topology and spectrum. They demonstrate that many observables exhibit leading $O(a^4)$ discretization errors, enabling reliable continuum extrapolations at larger lattice spacings than on the cubic lattice and yielding improved chiral and topological properties. The results indicate substantial potential computational savings and motivate extending the study to fully dynamical QCD.

Abstract

We formulate QCD discretized on the four dimensional 16-cell honeycomb. The advantage is a higher degree of rotational symmetry as compared to a traditional cubic lattice leading to much smaller cut-off effects. We demonstrate in quenched QCD, through both gluonic and fermionic observables, that the scaling properties are indeed superior to the cubic lattice and much larger lattice spacings are sufficient for controlled continuum extrapolations. Chiral and topological properties also show remarkable improvement.

Figures (8)

• Figure 1: Distribution of the topological charge on the 16-cell honeycomb. For clarity we do not show the corresponding histogram with the cubic lattice, but as can be expected, the $a=0.12$ fm lattice spacing is too large for clear peaks in that case.
• Figure 2: Continuum limit of the topological susceptibility. Solid lines show the extrapolations; see text for details.
• Figure 3: Comparison of the free Wilson-Dirac spectra on lattice volumes $16^4$.
• Figure 4: The pressure as a function of $N_t$ normalized by the continuum values. The solid lines show the analytic ${\cal O}(1/N_t^2)$ and ${\cal O}(1/N_t^4)$ scalings of the two discretizations given by eqn (\ref{['pressure']}).
• Figure 5: Comparison of quenched Wilson-Dirac spectra on $12^4$ lattice volumes. For the cubic case we also show results on a finer, $24^4$ lattice. Each spectrum corresponds to a single configuration.