On early onset of quark number density at zero temperature

TL;DR

This paper investigates the early onset of quark number density at zero temperature in lattice QCD, revealing that the energy gap in the eigenvalue spectrum triggers the nonzero density once the chemical potential exceeds it.

Contribution

The authors introduce a physical parametrization of eigenvalues in the fermion determinant reduction formula, clarifying the mechanism behind early quark density onset at zero temperature.

Findings

Eigenvalues correspond to quark energy states.

The energy gap causes fermion determinant to be μ-independent below a threshold.

Quark number density becomes nonzero once μ exceeds the energy gap.

Abstract

We study a longstanding problem in lattice QCD at low temperature and nonzero quark chemical potential on an onset of the quark number density at $\mu=m_\pi/2$. We introduce a physical parametrization of the eigenvalues in the reduction formula of the fermion determinant. It is shown that the parametrization reduces the quark number density operator to an expression with the Fermi distribution of the quark. For each configuration, the eigenvalues of the reduced matrix correspond to one-particle energy states of a quark. The gap of the eigenspectrum of the reduced matrix corresponds to the gap of the energy states, which causes the $\mu$-independence of the fermion determinant for small $\mu$ at T=0. Once $\mu$ exceeds the gap, the quark number density becomes nonzero for each configuration, which causes the early onset of the quark number density.