Dirac-mode analysis for quark number density and its application for deconfinement transition

TL;DR

This paper explores the behavior of quark number density at finite imaginary chemical potential using Dirac-mode expansion in lattice QCD, revealing its dependence on Dirac modes and implications for deconfinement transition.

Contribution

It provides an analytical formula relating quark number density to the Polyakov loop and investigates the mode dependence of quark number density in lattice QCD.

Findings

Quark number density strongly depends on low-lying Dirac modes in small quark mass regime.

Quark number holonomy is insensitive to low-lying Dirac modes.

The study offers insights into the confinement-deconfinement transition mechanisms.

Abstract

The quark number density at finite imaginary chemical potential is investigated in the lattice QCD using the Dirac-mode expansion. We find the analytical formula of the quark number density in terms of the Polyakov loop in the large quark mass regime. On the other hand, in the small quark mass region, the quark number density is investigated by using the quenched lattice QCD simulation. The quark number density is found to strongly depend on the low-lying Dirac modes while its sign does not change. This result leads to that the quark number holonomy is not sensitive to the low-lying Dirac modes. We discuss the confinement-deconfinement transition from the property of the quark number density and the quark number holonomy.