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

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 $107 \, \mathrm{MeV}$.