The phase structure of lattice QCD with two flavours of Wilson quarks and renormalization group improved gluons

TL;DR

The paper investigates how RG-improved gauge action (DBW2) affects the near-zero quark-mass phase structure of two-flavor Wilson QCD by contrasting it with the Wilson plaquette action at matched lattice spacings. It employs Wilson fermions with a twisted mass and uses the TSMB updating algorithm to measure masses, twist angles, topological charge, and eigenvalue spectra on $8^3\times16$ and $12^3\times24$ lattices. The findings show that DBW2 smooths the phase structure, reduces the minimal pion mass and the plaquette jump between coexisting phases, and can eliminate metastability at nonzero twisted mass; topological transitions slow down but remain tractable, and the eigenvalue spectrum shifts toward closer-to-origin values. These results imply improved reliability and efficiency for Wilson-type simulations with RG-improved gluons, while leaving open questions about the dependence on β (lattice spacing) and scaling toward the continuum.

Abstract

The effect of changing the lattice action for the gluon field on the recently observed [1] first order phase transition near zero quark mass is investigated by replacing the Wilson plaquette action by the DBW2 action. The lattice action for quarks is unchanged: it is in both cases the original Wilson action. It turns out that Wilson fermions with the DBW2 gauge action have a phase structure where the minimal pion mass and the jump of the average plaquette are decreased, when compared to Wilson fermions with Wilson plaquette action at similar values of the lattice spacing. Taking the DBW2 gauge action is advantageous also from the point of view of the computational costs of numerical simulations.

Figures (14)

• Figure 1: The schematic view of the first order phase transition surface in the $(\beta,\kappa,\mu)$ space close to the continuum limit. ($\beta$=bare gauge coupling, $\kappa$=hopping parameter, $\mu$=bare twisted quark mass, $\mu_\kappa \equiv (2\kappa)^{-1}$=bare untwisted quark mass.) The crosses mark the second order boundary line of the first order phase transition surface. The strong coupling region near $\beta=0$ is not shown in this figure.
• Figure 2: Upper panels: the signals of the $N_t=4$ non-zero temperature transition on an $8^3\times 4$ lattice with the DBW2 gauge action. Lower panels: the same with Wilson gauge action. Left panels: absolute value of the Polyakov line, right panels: average Wilson loop, both as a function of $\kappa$.
• Figure 3: Results of the numerical simulation on an $8^3\times 16$ lattice at $\beta=0.55$: upper panel the square of the pion mass $(am_\pi)^2$, lower panel the PCAC quark mass $am_\chi^{PCAC}$. In the upper panel the dashed lines are extrapolations to zero pion mass: at right it is a linear fit of four points, at left a straight line connecting two points with small quark mass.
• Figure 4: The average plaquette at $\beta=0.67$ on a $12^3\times 24$ lattice as a function of the hopping parameter $\kappa$: upper panel $\mu=0$ and lower panel $\mu=0.01$, respectively.
• Figure 5: Results of the numerical simulation on a $12^3\times 24$ lattice at $\beta=0.67$ as a function of $\mu_\kappa=(2\kappa)^{-1}$: upper panels $\mu=0$, lower panels $\mu=0.01$. Left panels: $(a m_\pi)^2$, right panels: the bare PCAC quark mass $am_\chi^{PCAC}$. The straight lines are fits to the points in the positive and negative quark mass phase, respectively. The horizontal line in the upper left panel shows the estimated value of the minimal pion mass in lattice units. The straight lines in the right panels are explained in the text.