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We investigate the Dirac eigenvalue spectrum ($\rho(\lambda,m_l)$) to studythe microscopic origin of axial anomaly in high temperature phase of QCD. Wepropose novel relations between the derivatives ($\partial^n\rho(\lambda,m_l)/\partial m_l^n$) of the Dirac eigenvalue spectrum withrespect to the quark mass ($m_l$) and the $(n+1)$-point correlations among theeigenvalues ($\lambda$) of the massless Dirac operator. Based on theserelations, we present lattice QCD results for $\partial^n\rho(\lambda,m_l)/\partial m_l^n$ ($n=1, 2, 3$) with $m_l$ corresponding topion masses $m_\pi=160-55$ MeV, and at a temperature of about 1.6 times thechiral phase transition temperature. Calculations were carried out using(2+1)-flavors of highly improved staggered quarks and the tree-level Symanzikgauge action with the physical strange quark mass, three lattice spacings$a=0.12, 0.08, 0.06$ fm, and lattices having aspect ratios $4-9$. We find that$\rho(\lambda\to0,m_l)$ develops a peaked structure. This peaked structure,which arises due to non-Poisson correlations within the infrared part of theDirac eigenvalue spectrum, becomes sharper as $a\to0$, and its amplitude isproportional to $m_l^2$. After continuum and chiral extrapolations, we findthat the axial anomaly remains manifested in two-point correlation functions ofscalar and pseudo-scalar mesons in the chiral limit. We demonstrate that thebehavior of $\rho(\lambda\to0,m_l)$ is responsible for it.

Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD