[Paper Review] Four Flavor Finite Temperature Phase Transition with HYP Action: Where is the First Order Phase Transition Line?

Anna Hasenfratz, Francesco Knechtli|ArXiv.org|May 19, 2001

High-Energy Particle Collisions Research3 citations

TL;DR

This paper investigates the finite-temperature phase transition in four-flavor QCD using staggered fermions with HYP-smeared gauge links, introducing a new efficient algorithm for simulating these improved actions. It finds that enhanced flavor symmetry from HYP smearing suppresses the first-order chiral phase transition observed in thin-link simulations, resulting in a smooth crossover-like transition without evidence of a first-order line even at physical quark masses on $N_t=4$ and $N_t=6$ lattices.

ABSTRACT

We study the finite temperature phase transition of four flavor staggered fermions with hypercubic fat link actions on N_t=4 and N_t=6 temporal lattices. Our fat links are constructed with hypercubic blocking (HYP) and therefore are very compact. We present a new algorithm for simulating fermions coupled to HYP fat links. The algorithm has a simple form based on the standard overrelaxation and heatbath updatings for the pure gauge action. We observe that as we increase the smoothness of the gauge fields by changing the parameters of the blocking the very pronounced first order phase transition of the thin link action becomes weaker and moves to physically uninteresting values of the gauge coupling. With our smoothest HYP action we do not find any indication of a phase transition in the accessible temperature range on the N_t=4 or 6 lattices even at quark masses close to the physical light quark mass. We argue that the observed difference in the phase diagram is due to the improved flavor symmetry of the smeared link actions.

Motivation & Objective

• To study the finite-temperature phase structure of four-flavor QCD with improved gauge link smearing using the HYP action.
• To develop an efficient simulation algorithm for HYP-smeared fermionic actions on $N_t=4$ and $N_t=6$ lattices.
• To determine whether the first-order chiral phase transition seen in thin-link staggered fermion simulations persists with improved flavor symmetry.
• To assess the impact of lattice spacing and flavor symmetry breaking on the location and nature of the chiral phase transition.
• To evaluate whether HYP-smeared actions correctly reproduce the expected chiral phase diagram at physical quark masses.

Proposed method

• Employed hypercubic blocking (HYP) to construct compact, flavor-symmetric fat links, reducing lattice artifacts in staggered fermion actions.
• Developed a new simulation algorithm based on standard overrelaxation and heatbath updates for the pure gauge action, adapted for HYP-smeared fermions.
• Performed simulations on $16^3 \times N_t$ lattices with $N_t=4$ and $N_t=6$, using quark masses $am_q \approx 0.0067$ to match physical light quark masses.
• Measured the Polyakov loop and chiral condensate $\langle \bar{\psi}\psi \rangle$ as functions of $\beta$ to identify phase transitions.
• Analyzed the susceptibility $\chi_{\bar{\psi}\psi,\,\text{disc}}$ to detect peaks indicative of first-order transitions.
• Compared results across $N_t=4$ and $N_t=6$ lattices and with different gauge couplings to assess scaling and finite-size effects.

Experimental results

Research questions

• RQ1 Does the first-order chiral phase transition in four-flavor QCD persist when using HYP-smeared gauge links with improved flavor symmetry?
• RQ2 How does the HYP smearing procedure affect the location and strength of the chiral phase transition compared to thin-link actions?
• RQ3 Can the HYP-smeared action reproduce the expected crossover behavior at physical quark masses on $N_t=4$ and $N_t=6$ lattices?
• RQ4 What is the impact of lattice spacing (via $N_t$) on the phase structure when using chirally improved fermion actions?
• RQ5 Does the improved topological structure from HYP actions eliminate the lattice artifacts that obscure the true phase diagram in thin-link simulations?

Key findings

• The HYP1-smeared action shows no sign of a first-order phase transition on $N_t=4$ or $N_t=6$ lattices, even at quark masses near the physical light quark mass.
• The Polyakov loop and chiral condensate vary smoothly with $\beta$, indicating a crossover rather than a first-order transition.
• The susceptibility $\chi_{\bar{\psi}\psi,\,\text{disc}}$ shows no peak in the accessible range, further supporting the absence of a first-order transition.
• The critical region shifts to higher $\beta$ values on $N_t=6$ compared to $N_t=4$, with a $\Delta\beta \approx 0.2$ shift needed to match results across $N_t$ values.
• The chiral condensate normalized by quark mass, $\langle \bar{\psi}\psi \rangle / m_q$, agrees between $N_t=6$ and $N_t=4$ simulations when shifted by $\Delta\beta \approx 0.2$.
• The results suggest that improved flavor symmetry from HYP smearing suppresses the first-order transition, likely due to the presence of 15 near-degenerate Goldstone bosons.