New approach to canonical partition functions computation in $N_f=2$ lattice QCD at finite baryon density

TL;DR

This paper introduces a new numerical method for calculating canonical partition functions in lattice QCD at finite baryon density, validated through comparison with existing approaches across different phases.

Contribution

The authors develop a novel procedure combining numerical fitting and Fourier transformation to compute canonical partition functions, validated against the hopping parameter expansion method.

Findings

The new method produces results consistent with established techniques.

It is effective in both confining and deconfining phases.

Numerical results confirm the method's validity.

Abstract

We propose and test a new approach to computation of canonical partition functions in lattice QCD at finite density. We suggest a few steps procedure. We first compute numerically the quark number density for imaginary chemical potential $i\mu_{qI}$. Then we restore the grand canonical partition function for imaginary chemical potential using fitting procedure for the quark number density. Finally we compute the canonical partition functions using high precision numerical Fourier transformation. Additionally we compute the canonical partition functions using known method of the hopping parameter expansion and compare results obtained by two methods in the deconfining as well as in the confining phases. The agreement between two methods indicates the validity of the new method. Our numerical results are obtained in two flavor lattice QCD with clover improved Wilson fermions.