Chiral Random Matrix Model for Critical Statistics

Abstract

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 non-interacting Fermi-gas we show that for energy differences less than a critical energy $E_c$ the spectral correlations are given by chiral Random Matrix Theory whereas for energy differences larger than $E_c$ 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.

21 pages, 3 figures, Latex; added two references and minor corrections

References in corpus (5)

• Fluctuations of the inverse participation ratio at the Anderson transition
• One-Dimensional String Theory with Vortices as Upside-Down Matrix Oscillator
• Effective Field Theory of the Random Flux Model
• Random Matrix Theory, Chiral Perturbation Theory, and Lattice Data
• Effects of Topology in the Dirac Spectrum of Staggered Fermions

Cited by in corpus (25)

• Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Critical statistics in quantum chaos and Calogero-Sutherland model at finite temperature
• Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature
• Power-law deformation of Wishart-Laguerre ensembles of random matrices
• Critical statistics for non-Hermitian matrices
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Statistics of the maximal distance and momentum in a trapped Fermi gas at low temperature
• Family of solvable generalized random-matrix ensembles with unitary symmetry
• Anderson transition in systems with chiral symmetry
• Non-interacting fermions in hard-edge potentials
• Eigenvalues of the QCD Dirac matrix with improved staggered quarks in the continuum limit
• Critical conductance of two-dimensional chiral systems with random magnetic flux
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Long range disorder and Anderson transition in systems with chiral symmetry
• The QCD vacuum as a disordered medium: A simplified model for the QCD Dirac operator
• Energy level statistics of a critical random matrix ensemble
• Two-level correlation function of critical random-matrix ensembles
• Heavy-tailed chiral random matrix theory
• Universality of a family of Random Matrix Ensembles with logarithmic soft-confinement potentials
• Spectral properties of a generalized chGUE
• Metal or Insulator? Dirac operator spectrum in holographic QCD
• Rotationally invariant family of Lévy like random matrix ensembles
• Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model
• Nonlinear sigma model approach for level correlations in chiral disordered systems