Finite temperature study of the axial U(1) symmetry on the lattice with overlap fermion formulation
We examine the axial U(1) symmetry near and above the finite temperature phase transition in two-flavor QCD using lattice QCD simulations. Although the axial U(1) symmetry is always violated by quantization, (i.e.) the chiral anomaly, the correlation functions may manifest effective restoration of the symmetry in the high temperature phase. We explicitly study this possibility by calculating the meson correlators as well as the Dirac operator spectral density near the critical point. Our numerical simulations are performed on a $16^3\times 8$ lattice with two flavors of dynamical quarks represented by the overlap fermion formalism. Chiral symmetry and its violation due to the axial anomaly is manifestly realized with this formulation, which is a prerequisite for the study of the effective restoration of the axial U(1) symmetry. In order to avoid discontinuity in the gauge configuration space, which occurs for the exactly chiral lattice fermions, the simulation is confined in a fixed topological sector. It induces finite volume effect, which is well described by a formula based on the Fourier transform from the $θ$-vacua. We confirm this formula at finite temperature by calculating the topological susceptibility in the quenched theory. Our two flavor simulations show degeneracy of the meson correlators and a gap in the Dirac operator spectral density, which implies that the axial U(1) symmetry is effectively restored in the chirally symmetric phase.