Actions for dynamical fermion simulations: are we ready to go?

TL;DR

This critical review assesses the readiness of dynamical fermion simulations in lattice QCD, outlining the spectrum of lattice actions, their locality properties, and perturbative foundations while highlighting major challenges such as phase transitions, nonlocal constructions, and escalating computational costs. It argues for a cautious, multi-action strategy, rigorous scaling tests in the quenched regime, and systematic cross-validation against chiral perturbation theory to ensure trustworthy continuum extrapolations. The work emphasizes the urgent need for algorithmic advances and cross-collaboration (e.g., ILDG) to overcome the cost barrier and to reliably determine fundamental QCD parameters with controlled systematic errors. Overall, it guides methodological choices and prioritizes targeted tests (locality, phase structure, topology) and the integration of chiral effective theories to bridge lattice results to phenomenology, particularly for $N_f=2+1$ dynamical simulations.

Abstract

A critical review, playing devil's advocate, on present dynamical fermion simulations is given.

Figures (11)

• Figure 1: A comparison of the cost of dynamical fermion simulations with (inexact) staggered (dotted line) and improved Wilson fermions (full line). The dashed line is the cost for Wilson fermions if the algorithms would perform a factor of four better than found in ukawa. The left plot is for a value of the lattice spacing $a=0.09$fm and the right plot for $a=0.045$fm.
• Figure 2: A comparison of the plaquette from an exact odd flavour simulation (triangles) and an in-exact one (circles, square) against the step-size $dt$, from the first reference of oddflavour.
• Figure 3: Continuum extrapolations of unimproved Wilson and unimproved staggered fermions, employing a pure $a^2$ dependence in the unimproved staggered and an $a+a^2$ dependence in the unimproved Wilson case. A fixed value of $m_{PS}/m_V=0.7$ was chosen. Also included are data for improved staggered, hypercube and FLIC fermions. The data were compiled together with J. Zanotti.
• Figure 4: Static potential for various gauge actions. Note that, as the effect of complex eigenvalues, in the case of improved gauge actions rgaction the potential starts from below.
• Figure 5: Thermal cycles in $\kappa$ for the plaquette for $N_f=3$ non-perturbatively improved Wilson fermions at various values of $\beta$ ranging from $\beta=4.6$ to $\beta=6$ from bottom to top (from cppacspd). For $\beta\approx 5$ hysteresis effects are observed, indicating the existence of a first order phase transition.