Chiral phase transition as an Anderson transition in the Instanton Liquid Model for QCD

We study the spectrum and eigenmodes of the QCD Dirac operator in a gauge background given by an Instanton Liquid Model (ILM) at temperatures around the chiral phase transition. For two massless quark flavors we observe that at the chiral phase transition, both the low lying eigenmodes and the spectrum of the QCD Dirac operator resemble those of a disordered conductor at the Anderson transition. In particular we present results showing that the eigenvectors are multifractal and the spectral correlations are well described by critical statistics. We also find an additional temperature dependent mobility edge located in the bulk of the spectrum with properties quantitatively similar to those of a 3D disordered conductor at the Anderson transition. This feature is present in both quenched and unquenched simulations. Finally we argue that our findings are not in principle restricted to the ILM approximation and may also be found in lattice simulations.