Twisted mass quarks and the phase structure of lattice QCD

TL;DR

This study investigates the zero-temperature phase structure of Wilson twisted mass QCD, uncovering strong metastabilities in the plaquette near the critical untwisted mass. By employing both HMC and TSMB algorithms at $\beta=5.2$, the authors observe coexisting metastable plaquette states and measure pion and PCAC masses to characterize the two branches. They interpret these findings within the framework of chiral symmetry breaking and the Sharpe-Singleton effective potential, arguing that lattice artifacts can induce first-order-like transitions or mimic near-critical behavior. The work highlights the need to map the phase diagram as a function of $\beta$ and $\mu$, and suggests that careful action choices or parameter tuning may mitigate metastabilities for phenomenologically relevant simulations.

Abstract

The phase structure of zero temperature twisted mass lattice QCD is investigated. We find strong metastabilities in the plaquette observable when the untwisted quark mass assumes positive or negative values. We provide interpretations of this phenomenon in terms of chiral symmetry breaking and the effective potential model of Sharpe and Singleton.

Figures (7)

• Figure 1: Thermal cycles in $\kappa$ on $8^3\times 16$ lattices at $\beta=5.2$. The plaquette expectation value is shown for: $a\mu=0.1$ (A); $a\mu=0.01$ (B); $a\mu=0$ (C). The triangles ($\triangledown$) refer to increasing $\kappa$-values, the diamonds ($\Diamond$) to decreasing ones.
• Figure 2: Metastable states at $\beta=5.2$. The number of sweeps is given in thousands. The lattice size is $12^3 \times 24$, except for the right panel in the bottom line where it is $16^3 \times 32$. The twisted mass is $a\mu=0.01$, except for the left panel in the bottom line where it is $a\mu=0$.
• Figure 3: The pion mass squared in lattice units on two lattice sizes measured separately on configurations in the two metastable states. These runs were made at $\beta=5.2$ and $a\mu=0.01$.
• Figure 4: The quark mass in lattice units $m_\chi^{\mathrm{PCAC}}$ as defined in eq. (\ref{['mpcac']}) on two lattice sizes measured separately on configurations in the two metastable states. The values of $\beta=5.2$ and $a\mu=0.01$ are fixed.
• Figure 5: The pion mass squared in lattice units from fig. \ref{['pionmass']} plotted against the untwisted PCAC quark mass in fig. \ref{['quarkmass']}.