Spectral density of the Dirac operator in two-flavor QCD

We compute the spectral density of the (Hermitian) Dirac operator in quantum chromodynamics with two light degenerate quarks near the origin. We use CLS/ALPHA lattices generated with two flavors of OðaÞ-improved Wilson fermions corresponding to pseudoscalar meson masses down to 190 MeVand with spacings in the range 0.05–0.08 fm. Thanks to the coverage of parameter space, we can extrapolate our data to the chiral and continuum limits with confidence. The results show that the spectral density at the origin is nonzero because the low modes of the Dirac operator do condense as expected in the Banks-Casher mechanism. Within errors, the spectral density turns out to be a constant function up to eigenvalues of ≈80 MeV. Its value agrees with the one extracted from the Gell-Mann-Oakes-Renner relation.