Phase Fluctuation of Fermion Determinant in Lattice QCD at Finite Density

TL;DR

This paper investigates phase fluctuations of the fermion determinant in finite density lattice QCD, analyzing their impact on physical observables and exploring symmetry considerations at small chemical potentials.

Contribution

It provides the first detailed calculation of phase fluctuations of the fermion determinant at finite density in SU(3) lattice QCD with 2 flavors, and examines their effect on key observables.

Findings

Little difference in chiral condensate and Polyakov line with phase reweighting at μ=0.1 and 0.2

Phase fluctuations are small at μ ≤ 0.27, possibly due to Z_3 symmetry

Phase fluctuation effects are negligible at small chemical potentials

Abstract

Once the quark chemical potential $\mu$ is introduced in finite density QCD, the fermion determinant appeared in the path integral measure becomes complex. In order to investigate the phase effect of SU(3) lattice QCD (2-flavors), we calculated the fluctuation of the phase of $\det\Delta(\mu)$ on a $8^3\times4$ lattice at $\mu = 0.1$ and 0.2. Then we calculated the chiral condensate and Polyakov line in the no phase and reweighted cases. There is little difference between these two cases at $\mu = 0.1$ and 0.2. We consider a possible reason for this result below $\mu \le 0.27$ in terms of $Z_3$ symmetry.