  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. Generically we find the Dirac eigenvectors become more
localized as the temperature is increased. At the chiral phase transition, both
the low lying eigenmodes and the spectrum of the QCD Dirac operator undergo a
transition to localization similar to the one observed in a disordered
conductor. This suggests that Anderson localization is the fundamental
mechanism driving the chiral phase transition. We also find an additional
temperature dependent mobility edge (separating delocalized from localized
eigenstates) in the bulk of the spectrum which moves toward lower eigenvalues
as the temperature is increased. In both regions, the origin and the bulk, the
transition to localization exhibits features of a 3D Anderson transition
including multifractal eigenstates and spectral properties that are well
described by critical statistics. Similar results are obtained in both the
quenched and the unquenched case though the critical temperature in the
unquenched case is lower. Finally we argue that our findings are not in
principle restricted to the ILM approximation and may also be found in lattice
simulations.
