Low temperature limit of lattice QCD

TL;DR

This paper investigates the behavior of lattice QCD at low temperatures using a reduction formula for the fermion determinant, revealing eigenvalue scaling laws and different determinant expressions depending on quark chemical potential.

Contribution

It introduces a scaling law for eigenvalues of the reduced matrix in low temperature lattice QCD and derives corresponding fermion determinant expressions for varying chemical potentials.

Findings

Eigenvalues follow a specific scaling law with respect to N_t.

Two distinct fermion determinant expressions are derived for different chemical potential regimes.

The results enhance understanding of low temperature behavior in finite density lattice QCD.

Abstract

We study the low temperature limit of lattice QCD by using a reduction formula for a fermion determinant. The reduction formula, which is useful in finite density lattice QCD simulations, contains a reduced matrix defined as the product of $N_t$ block-matrices. It is shown that eigenvalues of the reduced matrix follows a scaling law with regard to the temporal lattice size $N_t$. The $N_t$ scaling law leads to two types of expressions of the fermion determinant in the low temperature limit; one is for small quark chemical potentials, and the other is for larger quark chemical potentials.