Critical behaviour in the QCD Anderson transition

Abstract

We study the Anderson-type localisation-delocalisation transition found previously in the QCD Dirac spectrum at high temperature. Using high statistics QCD simulations with N f = 2 + 1 flavours of staggered quarks, we discuss how the change in the spectral statistics depends on the volume, the temperature and the lattice spacing, and we speculate on the possible universality of the transition from Poisson to Wigner-Dyson in the spectral statistics. Moreover, we show that the transition is a genuine phase transition: at the mobility edge, separating localised and delocalised modes, quantities characterising the spectral statistics become non-analytic in the thermodynamic limit. Using finite size scaling we also determine the critical exponent of the correlation length, and we speculate on possible extensions of the universality of Anderson transitions.

Critical statistics at the mobility edge of QCD Dirac spectra

“…We showed that the level spacing statistics across the Anderson-type transition in the QCD staggered-Dirac spectrum can be described by the same deformed RM ensemble that describes the transition in the Anderson model. Together with the compatibility of the critical exponents of these two models [47], our result lends further support to the idea that these two transitions indeed belong to the same universality class. Further confirmation of our findings in the case of Ginsparg-Wilson Dirac operators [42], close to the physical point, would be an important next step.…”

Chiral transition as Anderson transition

“…In the same work we also determined the critical exponent ν QCD = 1.43 (6) which is consistent with the one found in the three dimensional unitary Anderson model ν And = 1.43 (4) [10]. A possible explanation for this consistency, and a more detailed description of the similarities of the spectra of the Anderson model and of the QCD Dirac operator can be found in [11]. In the Anderson model the control parameter which drives the transition is the disorder strength σ (ε i ).…”

Quark localization in QCD above $T_c$

“…It is clearly seen that the transition becomes sharper for larger volumes, which suggests that it becomes a true phase transition in the thermodynamic limit. A proper finite size scaling analysis of the transition and a comparison with the Anderson transition is discussed in [10]. In a finite volume the separation between localized and delocalized modes is not sharp, and so the definition of the "mobility edge" λ c is not unique.…”