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Abstract
We study the finite temperature localization transition in the spectrum of the overlap Dirac operator. Simulating the quenched approximation of QCD, we calculate the mobility edge, separating localized and delocalized modes in the spectrum. We do this at several temperatures just above the deconfining transition and by extrapolation we determine the temperature where the mobility edge vanishes and localized modes completely disappear from the spectrum. We find that this temperature, where even the lowest Dirac eigenmodes become delocalized, coincides with the critical temperature of the deconfining transition. This result, together with our previously obtained similar findings for staggered fermions shows that quark localization at the deconfining temperature is independent of the fermion discretization, suggesting that deconfinement and localization of the lowest Dirac eigenmodes are closely related phenomena.
Highlights
Interacting matter is known to undergo a crossover at high temperature
We compared our result with the critical coupling of the deconfining phase transition and found that the two critical couplings are compatible; the localization transition and deconfinement occur at the same temperature
The present work was motivated by the fact that in QCD with physical dynamical quarks the localization transition occurs in the crossover region
Summary
Interacting matter is known to undergo a crossover at high temperature. In the low temperature regime, quarks are bound together to form hadrons due to color confinement. The staggered Dirac operator is expected to have the correct continuum limit, it is still possible that at finite lattice spacing it does not properly describe some properties of the lowest quark eigenmodes, the ones that are our main concern here for studying the localization transition. This is a potentially important issue, as the lowest part of the Dirac spectrum is sensitive to the chiral properties of the given discretization. IV, we draw our conclusions and in the Appendix we describe the technical details of the unfolding of the spectrum
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