  We study the restoration of the spontaneously broken chiral symmetry and the
anomalously broken axial U(1) symmetry in finite temperature QCD at zero
chemical potential. We use 2 flavors lattice QCD with optimal domain-wall
fermion on the $ 16^3 \times 6 $ lattice, with the extent $ N_s = 16 $ in the
fifth dimension, in the temperature range $ T = 130-230 $ MeV. To examine the
restoration of the chiral symmetry and the axial $ U(1) $ symmetry, we use
diluted $ Z_2 $ noises to calculate the chiral condensate, and the chiral
susceptibilities in the scalar and pseudoscalar meson channels, for flavor
singlet and non-singlet respectively. From the degeneracy of the chiral
susceptibilities around $ T_c $, it suggests that the axial $ U(1) $ symmetry
is restored in the chirally symmetric phase. Moreover, we examine the spectral
density $ \rho(\lambda_c) $ of the 4D effective Dirac operator with exact
chiral symmetry, which is obtained by computing zero modes plus (180+180)
conjugate pairs of low-lying modes for each gauge configuration. The
suppression of low modes in the spectral density provides a consistency check
of the restoration of axial $ U(1) $ symmetry in the chirally symmetric phase.
