Solution of the Complex Action Problem in the Potts Model for Dense QCD

TL;DR

This paper addresses the complex action problem in lattice QCD at finite chemical potential by solving it in the 3-state Potts model using a cluster algorithm, enabling the study of phase transitions and potentials at non-zero density.

Contribution

The authors introduce a cluster algorithm that solves the complex action problem in the Potts model, allowing for detailed analysis of phase transitions in dense QCD.

Findings

Localization of the critical endpoint consistent with 3-d Ising universality

Identification of screening in static potentials at non-zero density

Validation of the Potts model as an effective theory near deconfinement

Abstract

Monte Carlo simulations of lattice QCD at non-zero baryon chemical potential $\mu$ suffer from the notorious complex action problem. We consider QCD with static quarks coupled to a large chemical potential. This leaves us with an SU(3) Yang-Mills theory with a complex action containing the Polyakov loop. Close to the deconfinement phase transition the qualitative features of this theory, in particular its Z(3) symmetry properties, are captured by the 3-d 3-state Potts model. We solve the complex action problem in the Potts model by using a cluster algorithm. The improved estimator for the $\mu$-dependent part of the Boltzmann factor is real and positive and is used for importance sampling. We localize the critical endpoint of the first order deconfinement phase transition line and find consistency with universal 3-d Ising behavior. We also calculate the static quark-quark, quark-anti-quark, and anti-quark-anti-quark potentials which show screening as expected for a system with non-zero baryon density.