Scaling study of dynamical smeared-link clover fermions

TL;DR

This work demonstrates that combining six-step stout-link smearing with a tree-level Symanzik gauge action and a stout-clover fermion formulation yields an ultralocal, efficiently simulable lattice QCD framework. Using HMC for two flavors and RHMC for the third, along with multiple time-scale integration, mass preconditioning, Omelyan integration, and mixed-precision solvers, the authors perform a detailed scaling study in $N_f=3$ QCD along lines of constant physics $M_\pi/M_\rho$, finding a robust scaling region down to $a\lesssim 0.16-0.19$ fm. The analysis shows small discretization errors in the baryon spectrum, smooth continuum extrapolations for $M_N$ and $M_\Delta$, and ergodic sampling of topology with no metastability or exceptional configurations observed even at relatively light quark masses. Overall, the results support the use of smeared-link clover actions for large-scale phenomenological investigations in $N_f=2+1$ QCD and likely extend to other comparable smeared actions.

Abstract

We present a framework for phenomenological lattice QCD calculations which makes use of a tree level Symanzink improved action for gluons and stout-link Wilson fermions. We give details of our efficient HMC/RHMC algorithm and present a scaling study of the low-lying N_f=3 baryon spectrum. We find a scaling region that extends to a~<0.16fm and conclude that our action and algorithm are suitable for large scale phenomenological investigations of N_f=2+1 QCD. We expect this conclusion to hold for other comparable actions.

Figures (9)

• Figure 1: Performance of CG in double precision (squares) compared to a mixed precision variant of CG (circles). Data are from an $N_f=2+1$ run on a $32^3\times 64$ lattice at $\beta=3.57$ with $am_{ud}^\mathrm{PCAC}\simeq 0.0077$ and $am_{s}^\mathrm{PCAC}\simeq 0.049$ corresponding to $M_\pi\sim 250$ MeV.
• Figure 2: The magnitude of the smallest eigenvalue of the preconditioned hermitean Dirac operator in units of the PCAC mass. At each $\beta$ the lightest run ($M_\pi/M_\rho\simeq0.6$) is shown.
• Figure 3: Histogram of the inverse iteration number of our linear solver at a lighter $M_\pi$ for the lightest pseudofermion in the action. Results are from an $N_f = 2+1$ run on a $48^3\times 64$ lattice at $\beta = 3.57$ with $am_{ud}^{PCAC}\simeq 0.0056$ and $am_{s}^{PCAC}\simeq 0.044$ corresponding to $M_\pi\sim 190$ MeV.
• Figure 4: Absence of hysteresis in the average expectation value of the plaquette. Data are from an $N_f=2+1$ run on a $16^3\times 32$ lattice at $\beta=3.3$ with a fixed strange quark mass $am_s^\mathrm{PCAC}\simeq 0.0677$ and the light quark mass varying between $am_{ud}^\mathrm{PCAC}\simeq0.0066$ and $0.0243$ in ascending (square) and descending (circles) order. The range of light quark masses corresponds to $M_\pi\sim 240-440$ MeV. The second data set is slightly offset along the $x$-axis for better readability.
• Figure 5: History of the unrenormalized gluonic topological charge (left) and the corresponding autocorrelation function plot (right), measured on our finest lattice with the smallest quark mass: $\beta=3.76, aM_\pi=0.2019(20)$. The integrated autocorrelation time of $q_\mathrm{nai}$ is approximately $2$ configurations on this ensemble. A separation of one configuration corresponds to 10 HMC/RHMC trajectories.