Dirac Eigenvalue Spectrum at Finite Temperature Using Domain Wall Fermions

Abstract: We present a study of the Dirac eigenvalue spectrum near the region of the QCD phase transition. This study makes use of a sequence of ensembles with temperatures from 150 MeV to 200 MeV generated with $2 + 1$ flavors of dynamical domain wall fermions (DWF) and the dislocation sup- pressing determinant ratio (DSDR) action on a $16^3\times 8$ lattice with an extent of 32 or 48 in the fifth dimension. All the simulations lie on a line of constant physics with 200 MeV pions. The DWF Dirac operator is normalized using the methods of Giusti and Luscher combined with those of Rome-Southampton collaboration, allowing a direct evaluation of the Banks-Casher relation. The relation between the resulting temperature-dependent Dirac eigenvalue spectrum and the possible restoration of $U(1)_A$ symmetry with increasing temperature is discussed.