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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>N</a:mi> <a:mi mathvariant="normal">t</a:mi> </a:msub> <a:mo>=</a:mo> <a:mn>8</a:mn> </a:math> lattices we find that localized low modes, absent at low temperature, appear at a temperature <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msub> <d:mi>T</d:mi> <d:mi>loc</d:mi> </d:msub> </d:math> in the range <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mn>150</f:mn> <f:mtext> </f:mtext> <f:mtext> </f:mtext> <f:mi>MeV</f:mi> <f:mo>≤</f:mo> <f:msub> <f:mi>T</f:mi> <f:mi>loc</f:mi> </f:msub> <f:mo>≤</f:mo> <f:mn>160</f:mn> <f:mtext> </f:mtext> <f:mtext> </f:mtext> <f:mi>MeV</f:mi> </f:math> , 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 <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi>N</h:mi> <h:mi mathvariant="normal">t</h:mi> </h:msub> <h:mo>=</h:mo> <h:mn>8</h:mn> </h:math> , our conclusion that <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>T</k:mi> <k:mi>loc</k:mi> </k:msub> </k:math> is in the chiral crossover region is expected to remain valid in the continuum limit.