Thermodynamic Potential of the Polyakov Loop in SU(3) Quenched Lattice QCD

TL;DR

This paper calculates the thermodynamic potential of the Polyakov loop in SU(3) quenched lattice QCD at the critical temperature, revealing the structure of vacua during the deconfinement transition.

Contribution

It introduces a novel field-theoretical approach to determine the Polyakov loop effective potential at finite temperature in lattice QCD, especially at the critical point.

Findings

Effective potential clearly depicted around different vacua.

Vacuum-associated reweighting method successfully applied.

Results provide insights into vacuum structure at T_c.

Abstract

Using SU(3) lattice QCD, we study for the first time the effective potential of the Polyakov loop $\langle P \rangle$ at finite temperature, i.e., the thermodynamic potential, in the field-theoretical way. In the framework of the reweighting method in lattice QCD, we express the effective potential $V_{\rm eff}(\langle P \rangle)$ using the expectation value without a source term. In particular, we consider the most difficult and interesting case of vacuum coexistence at the critical temperature $T_c$. We adopt SU(3) quenched lattice QCD on $48^3 \times 6$ at $\beta$= 5.89379, which corresponds exactly to the critical temperature $T_c$ of the deconfinement phase transition, and use 200,000 Monte Carlo configurations. After categorizing the gauge configurations into one $Z_3$-symmetric and three $Z_3$-broken vacua each, we perform a vacuum-associated reweighting method, using the gauge configurations around each vacuum separately. Finally, we obtain the Polyakov-loop effective potential, which is well depicted around the $Z_3$-symmetric and $Z_3$-broken vacua.