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We investigate the low-lying eigenmodes of the Dirac matrix with the aim togain more insight into the temperature dependence of the anomalous $U_A(1)$symmetry. We use the overlap operator to probe dynamical QCD configurationsgenerated with (2+1)-flavors of highly improved staggered quarks. We find noevidence of a gap opening up in the infrared region of the eigenvalue spectrumeven at $1.5\,T_c$, $T_c$ being the chiral crossover temperature. Instead, weobserve an accumulation of near-zero eigenmodes. We argue that these near-zeroeigenmodes are primarily responsible for the anomalous breaking of the axialsymmetry still being effective. At $1.5\,T_c$, these near-zero eigenmodesremain localized and their distribution is consistent with the dilute instantongas picture. At this temperature, the average size of the instantons is$0.223(8)\,\text{fm}$ and their density is $0.147(7)\,\text{fm}^{-4}$.

Microscopic Origin of \boldmath{$U_A(1)$} Symmetry Violation in the High Temperature Phase of QCD