Sign problem in $Z_3$-symmetric effective Polyakov-line model

Abstract

As an effective model corresponding to $Z_3$-symmetric QCD ($Z_3$-QCD), we construct a $Z_3$-symmetric effective Polyakov-line model ($Z_3$-EPLM) by using the logarithmic fermion effective action. Since $Z_3$-QCD tends to QCD in the zero temperature limit, $Z_3$-EPLM also agrees with the ordinary effective Polyakov-line model (EPLM) there; note that ordinary EPLM does not possess $Z_3$ symmetry. Our main purpose is to discuss a sign problem appearing in $Z_3$-EPLM. The action of $Z_3$-EPLM is real, when the Polyakov line is not only real but also its $Z_3$ images. This suggests that the sign problem becomes milder in $Z_3$-EPLM than in EPLM. In order to confirm this suggestion, we do lattice simulations for both EPLM and $Z_3$-EPLM by using the reweighting method with the phase quenched approximation. In the low-temperature region, the sign problem is milder in $Z_3$-EPLM than in EPLM. We also propose a new reweighting method. This makes the sign problem very weak in $Z_3$-EPLM.

arXiv comment16 pages, 38 figures

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• Vacuum structure of Yang-Mills theory as a function of $\theta$
• High-temperature domain walls of QCD with imaginary chemical potentials
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• Persistent homology analysis of deconfinement transition in effective Polyakov-line model
• Nonanalyticity, sign problem and Polyakov line in Z3-symmetric heavy quark model at low temperature: Phenomenological model analyses