Canonical fermion determinants in lattice QCD - Numerical evaluation and properties

TL;DR

This paper investigates canonical fermion determinants in lattice QCD, revealing their strong dependence on center sectors of the Polyakov loop in the deconfined phase and analyzing their temperature-dependent distribution.

Contribution

It introduces a numerical method for computing canonical fermion determinants and explores their properties across different temperature regimes in pure SU(3) gauge configurations.

Findings

Canonical determinants strongly reflect center sector behavior in the deconfined phase.

The distribution of quark sectors varies significantly with temperature.

The study provides insights into the physical implications of fermion determinant behavior.

Abstract

We analyze canonical fermion determinants, i.e., fermion determinants projected to a fixed quark number q. The canonical determinants are computed using a dimensional reduction formula and are studied for pure SU(3) gauge configurations in a wide range of temperatures. It is demonstrated that the center sectors of the Polyakov loop very strongly manifest themselves in the behavior of the canonical determinants in the deconfined phase, and we discuss physical implications of this finding. Furthermore the distribution of the quark sectors is studied as a function of the temperature.