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We investigate the high-temperature phase of QCD using lattice QCDsimulations with $N_f = 2$ dynamical M\"obius domain-wall fermions. Ongenerated configurations, we study the axial $U(1)$ symmetry, overlap-Diracspectra, screening masses from mesonic correlators, and topologicalsusceptibility. We find that some of the observables are quite sensitive tolattice artifacts due to a small violation of the chiral symmetry. For thoseobservables, we reweight the M\"obius domain-wall fermion determinant by thatof the overlap fermion. We also check the volume dependence of observables. Ourdata near the chiral limit indicates a strong suppression of the axial $U(1)$anomaly at temperatures $\geq$ 220 MeV.

Axial U(1) symmetry and mesonic correlators at high temperature in $N_f=2$ lattice QCD