Microscopic origin of U-A(1) symmetry violation in the high temperature phase of QCD

We investigate the low-lying eigenmodes of the Dirac matrix with the aim to gain more insight into the temperature dependence of the anomalous U-A(1) symmetry in QCD. We use the overlap operator to probe dynamical QCD configurations generated with (2 + 1)-flavors of highly improved staggered quarks. We find no evidence of a gap opening up in the infrared region of the eigenvalue spectrum even at 1.5T(c), T-c being the chiral crossover temperature. Instead, we observe an accumulation of near-zero eigenmodes. We argue that these near-zero eigenmodes are primarily responsible for the anomalous breaking of the axial symmetry still being effective. At 1.5T(c), these near-zero eigenmodes remain localized and their distribution is consistent with the dilute instanton gas picture. At this temperature, the average size of the instantons is 0.223(8) fm and their density is 0.147(7) fm(-4).