Exploring the phase structure of lattice QCD with twisted mass quarks

TL;DR

This work analyzes the zero-temperature phase structure of lattice QCD with Wilson fermions in the twisted mass formulation for $N_f=2$. Through thermal cycles and long runs at $\beta=5.2$ with varying $\mu$ and $\kappa$, the authors observe metastabilities manifested as coexisting plaquette branches and opposite signs of the untwisted PCAC mass, indicating a first-order transition near $m_0\approx m_{\rm crit}$. A symmetry-based method is developed to determine the twist angle $\omega$ from parity constraints and Ward identities, revealing $\omega$ far from $\pi/2$ in the metastable region and approaching $\pi/2$ away from it. The results align with Wilson chiral perturbation theory predictions and suggest a spectral mechanism linked to the Wilson-fermion matrix near the origin, with implications for identifying safe parameter regions (e.g., $m_{\rm crit}$ and $\mu_c$) and understanding the impact of lattice actions and spacing on the phase structure.

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 sweeps across zero.

Figures (6)

• Figure 1: Thermal cycles in $\kappa$ on $8^3\times 16$ lattices at $\beta=5.2$. The plaquette expectation value is shown for: $\mu=0.1$ (A); $\mu=0.01$ (B); $\mu=0$ (C). The triangles refer to increasing $\kappa$-values, the diamonds to decreasing ones.
• Figure 2: Monte Carlo history of metastable states at $\beta=5.2$, $\mu=0.01$ and $\kappa=0.1717$. In the upper plot the lattice size is $16^3\times32$ and in the lower plot it is $12^3\times24$.
• Figure 3: Pseudoscalar mass as a function of $1/(2\kappa)$ at $\beta=5.2$ and $\mu=0.01$.
• Figure 4: $m_\chi^{\textrm{PCAC}}$ as a function of $1/(2\kappa)$ at $\beta=5.2$ and $\mu=0.01$.
• Figure 5: Twist angle as a function of $1/(2\kappa)$ at $\beta=5.2$ and $\mu=0.01$ in the two branches.