Non-trivial phase structure of $N_f=3$ QCD with $O(a)$-improved Wilson fermion at zero temperature

TL;DR

This work investigates the phase structure of $N_f=3$ QCD with $O(a)$-improved Wilson fermions using an exact algorithm for odd flavors. It maps the $(β,κ)$ phase diagram with a plaquette gauge action and finds a persistent first-order transition at zero temperature, which appears to be a lattice artifact. Replacing the gauge action with improved formulations (Iwasaki and Symanzik) removes the transition, highlighting the need for improved actions in realistic simulations. The study emphasizes practical implications for achieving feasible lattice spacings in $N_f=3$ QCD calculations and recommends adopting improved gauge actions accordingly.

Abstract

JLQCD collaboration recently started the $N_f=3$ QCD simulations with the $O(a)$-improved Wilson fermion action employing an exact fermion algorithm developed for odd number of quark flavors. It is found that this theory has an unexpected non-trivial phase structure in the $(β,κ)$ plane even at zero temperature. A detailed study is made to understand the nature of the observed phase transitions and to find the way of avoiding untolerably large lattice artifacts associated with the phase transition.

Figures (5)

• Figure 1: Thermal cycles on an $8^3 \times 16$ lattice at $\beta$ = 4.6, 4.8, 4.85, 4.9, 4.95, 5.0, 5.05, 5.1, 5.15, 5.2, 5.25, 5.3, 5.4, 5.6, 5.8, 6.0 from bottom to top.
• Figure 2: Two-state signals on a $12^3 \times 32$ lattice at $\beta$=4.88 and $c_{\mathrm{sw}}$=2.15.
• Figure 3: Phase diagram in $(\beta,\kappa)$ plane.
• Figure 4: Plaquette values in two phases at the first-order transition line as functions of $\beta$.
• Figure 5: Thermal cycle with RG gauge action at $\beta$=1.50$-$2.25 in steps of 0.05 (bottom to top).