Dirac mode localization in QCD near the crossover temperature

We study the localization properties of the low-lying Dirac eigenmodes in QCD near the crossover temperature, using stout-smeared staggered fermions and Symanzik-improved gauge action on the lattice. On $N_{\mathrm{t}}=8$ lattices we find that localized low modes, absent at low temperature, appear at a temperature $T_{\mathrm{l}\mathrm{o}\mathrm{c}}$ in the range $150\mathrm{M}\mathrm{e}\mathrm{V}\le T_{\mathrm{l}\mathrm{o}\mathrm{c}}\le 160\mathrm{M}\mathrm{e}\mathrm{V}$, well within the chiral crossover range as determined from the chiral condensate and from the light-quark susceptibility. Since with our choice of lattice action neither the chiral transition region nor the renormalized mobility edges change significantly above $N_{\mathrm{t}}=8$, our conclusion that $T_{\mathrm{l}\mathrm{o}\mathrm{c}}$ is in the chiral crossover region is expected to remain valid in the continuum limit.