The QCD vacuum as a disordered medium: A simplified model for the QCD Dirac operator

Abstract

We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of instantons. We compare the spectral correlations of this model to those of an instanton liquid model (ILM) and find agreement well beyond the Thouless energy. In the bulk of the spectrum the (dimensionless) Thouless energy of the RBM scales with the square root of system size in agreement with the ILM and chiral perturbation theory. Near the origin the scaling of the (dimensionless) Thouless energy in the RBM remains the same as in the bulk which agrees with chiral perturbation theory but not with the ILM. Finally we discuss how this RBM should be modified in order to describe the spectral correlations of the QCD Dirac operator at the finite temperature chiral restoration transition.

4 pages, 3 figures

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Cited by in corpus (10)

• New Trends in Density Matrix Renormalization
• Universal results from an alternate random matrix model for QCD with a baryon chemical potential
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Chiral phase transition and Anderson localization in the Instanton Liquid Model for QCD
• Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Deconfinement, chiral transition and localisation in a QCD-like model
• Anderson transition in systems with chiral symmetry
• Critical conductance of two-dimensional chiral systems with random magnetic flux
• Statistical properties of the critical eigenstates in power-law random banded matrices across the band