Dirac Spectral Density in N${}_f$=2+1 QCD at T=230 MeV

Abstract

We compute the renormalized Dirac spectral density in $N_f=2+1$ QCD at physical quark masses, temperature $T=230$ MeV and system size $L_s=3.4$ fm. To that end, we perform a point-wise continuum limit of the staggered density in lattice QCD with staggered quarks. We find, for the first time, that a clear infrared structure (IR peak) emerges in the density of Dirac operator describing dynamical quarks. We also provide numerical evidence that a component of this peak, which becomes dominant in the thermodynamic limit, is due to a non-trivial accumulation of near-zero modes. Features of this structure are consistent with those previously attributed to the recently-proposed IR phase of thermal QCD. Our results (i) provide the only complete first-principles evidence that these IR features exist and are physical; (ii) improve the upper bound for IR-phase transition temperature $T_{\mathrm{IR}}$ so that the new window is $200<T_{\mathrm{IR}}<230$MeV; (iii) are consistent with non-restoration of anomalous U${}_{\mathrm{A}}$(1) symmetry (chiral limit) below $T=230$ MeV.

Comments: 7 pages, 6 figures; v2: 8 pages, 7 figures, added results on the topological nature of the peak, other results and conclusions unchanged, version to appear in PRD