Chiral Random Matrix Model for Critical Statistics

We propose a random matrix model that interpolates between the chiral random matrix ensembles and the chiral Poisson ensemble. By mapping this model on a noninteracting Fermi-gas we show that for energy differences less than a critical energy Ec the spectral correlations are given by chiral Random Matrix Theory whereas for energy differences larger than Ec the number variance shows a linear dependence on the energy difference with a slope that depends on the parameters of the model. If the parameters are scaled such that the slope remains fixed in the thermodynamic limit, this model provides a description of QCD Dirac spectra in the universality class of critical statistics. In this way a good description of QCD Dirac spectra for gauge field configurations given by a liquid of instantons is obtained. PACS: 11.30.Rd, 12.39.Fe, 12.38.Lg, 71.30.+h