Chiral and deconfinement phase transition in the Hamiltonian approach to QCD in Coulomb gauge

TL;DR

This paper investigates the chiral and deconfinement phase transitions in QCD using a Hamiltonian approach in Coulomb gauge, calculating critical temperatures from the behavior of condensates as functions of temperature.

Contribution

It introduces a novel variational Hamiltonian method to study QCD phase transitions by encoding temperature dependence in the vacuum state on a compactified spatial dimension.

Findings

Chiral transition temperature: 168 MeV

Deconfinement transition temperature: 196 MeV

Method provides a new way to analyze QCD phase structure

Abstract

The chiral and deconfinement phase transitions are investigated within the variational Hamiltonian approach to QCD in Coulomb gauge. The temperature $\beta^{- 1}$ is introduced by compactifying a spatial dimension. Thereby the whole temperature dependence is encoded in the vacuum state on the spatial manifold $\mathbb{R}^2 \times S^1 (\beta)$. The chiral quark condensate and the dual quark condensate (dressed Polyakov loop) are calculated as function of the temperature. From their inflection points the pseudo-critical temperatures for the chiral and deconfinement crossover transitions are determined. Using the zero-temperature quark and gluon propagators obtained within the variational approach as input, we find $168 \, \mathrm{MeV}$ and $196 \, \mathrm{MeV}$, respectively, for the chiral and deconfinement transition.