Speaker
Description
Recently we developed an instanton-based random matrix model that precisely reproduces the lowest part of the spectrum of the lattice overlap Dirac operator, and in particular the details of the spectral peak at zero. Our model allows us to study the spectral peak for volumes and instanton densities that are several orders of magnitude beyond the possibilities of direct lattice calculations. We use this model to study the spectral peak, and show that in the peak the spectral density is power-law singular at zero with a power that depends on the instanton density and goes to -1 in the limit of zero density. We also demonstrate that very close to zero in the spectrum there is an additional, lower mobility edge and its location is also controlled by the instanton density. These features of the spectral peak are consistent with exact constraints on the Dirac spectrum derived from the expected pattern of chiral symmetry breaking/restoration, as well as lattice results.