Nonanalyticity, sign problem and Polyakov line in Z3-symmetric heavy quark model at low temperature: Phenomenological model analyses

TL;DR

This paper investigates the nonanalyticity and sign problem in a Z3-symmetric heavy quark model at low temperatures, analyzing the structure of zeros in the partition function and the effects of imaginary chemical potential.

Contribution

It provides a phenomenological analysis of the nonanalyticity and sign problem in Z3-symmetric models, connecting the zeros of the partition function with physical observables at low temperature.

Findings

The Polyakov line's average value detects the structure of zeros at nonanalytic points.

Thermodynamic quantities other than the Polyakov line are insensitive to the zero structure in the zero-temperature limit.

The imaginary quark chemical potential significantly influences the quark number density near nonanalytic points.

Abstract

The nonanalyticity and the sign problem in the Z3-symmetric heavy quark model at low temperature are studied phenomenologically. For the free heavy quarks, the nonanalyticity is analyzed in the relation to the zeros of the grand canonical partition function. The Z3-symmetric effective Polyakov-line model (EPLM) in strong coupling limit is also considered as an phenomenological model of Z3-symmetric QCD with large quark mass at low temperature. We examine how the Z3-symmetric EPLM approaches to the original one in the zero-temperature limit. The effects of the Z3-symmetry affect the structure of zeros of the microscopic probability density function at the nonanalytic point. The average value of the Polyakov line can detect the structure, while the other thermodynamic quantities are not sensible to the structure in the zero-temperature limit. The effect of the imaginary quark chemical potential is also discussed. The imaginary part of the quark number density is very sensitive to the symmetry structure at the nonanalytical point. For a particular value of the imaginary quark number chemical potential, large quark number may be induced in the vicinity of the nonanalytical point.