  The nature of chiral phase transition for QCD with two light quark flavors is
not yet completely resolved. This is primarily because one has to understand
whether or not the anomalous U(1) symmetry in the flavor sector is effectively
restored along with the chiral symmetry. Since the physics near the chiral
phase transition is essentially non-perturbative, we employ first principles
lattice techniques to address this issue. We use overlap fermions, which have
exact chiral symmetry on the lattice, to probe the anomalous U(1) symmetry
violation of 2+1 flavor dynamical QCD configurations with domain wall fermions.
The latter also optimally preserves chiral and flavor symmetries on the
lattice. We observe that the anomalous U(1) is not effectively restored in the
chiral crossover region. We perform a systematic study of the finite size and
cut-off effects since the signals of U(1) violation are sensitive to it. For
the same reasons we also compare our results from the continuum extrapolated
results of the QCD Dirac spectrum obtained from a different lattice
discretization called Highly Improved Staggered Quarks. Our studies also
provide a glimpse of the microscopic topological structures of the QCD medium
that are responsible for the strongly interacting nature of the quark gluon
plasma phase and related to the physics of confinement and chiral symmetry
breaking.
