Chiral symmetry restoration at finite temperature within the Hamiltonian approach to QCD in Coulomb gauge

TL;DR

This paper investigates the chiral phase transition in QCD at finite temperature using a Hamiltonian approach in Coulomb gauge, revealing a second-order transition at approximately 107 MeV.

Contribution

It introduces a novel method of studying finite-temperature QCD by compactifying a spatial dimension within the Hamiltonian framework, providing new insights into chiral symmetry restoration.

Findings

Identifies a second-order chiral phase transition at ~107 MeV.

Demonstrates the effectiveness of the Hamiltonian approach with spatial compactification.

Provides numerical solutions for the quark sector at finite temperature.

Abstract

The chiral phase transition of the quark sector of QCD is investigated within the Hamiltonian approach in Coulomb gauge. Finite temperatures $T$ are introduced by compactifying one spatial dimension, which makes all thermodynamical quantities accessible from the ground state on the spatial manifold $\mathbb{R}^2 \times S^1(1/T)$. In the limit of a vanishing quark-gluon coupling, the equations of motion of the quark sector are solved numerically and the chiral quark condensate is evaluated and compared to the results of the usual canonical approach to finite-temperature Hamiltonian QCD based on the density operator of the grand canonical ensemble. For zero bare quark masses, we find a second-order chiral phase transition with a critical temperature of about $107 \, \mathrm{MeV}$.