• lattice
• localization
• mobility edge
• QCD
• Roberge
• simulations
• transition
• Weiss

In this work we studied through lattice QCD simulations the localization transition in the eigenmodes of the QCD Dirac operator at the Roberge-Weiss point, where the theory has the only symmetry in presence of physical quark masses. This symmetry allows us to properly define deconfinement as the phase in which it is spontaneously broken. Numerical simulations showed that this happens above the critical temperature T_{RW} = 208(5) MeV, which we compared with our results about localization: we found that at low temperatures all the modes of the Dirac spectrum are delocalized, while above the critical temperature T_{l} its lowest part becomes localized, i.e. the modes spreads only in a fraction of the total four-volume. We computed T_{l} as the temperature at which the mobility edge, which is the boundary value of the eigenvalues between localized and delocalized states, vanishes: we calculated the mobility edges at different temperatures and extrapolated T_{l} with a fit. We performed the simulations on Nt*Ns^3 lattices and we computed T_{l} at each Nt: with these data we extrapolated the continuum limit T_{l} = 212(10) MeV, compatible with the Roberge-Weiss temperature.