Long range disorder and Anderson transition in systems with chiral symmetry

Abstract

We study the spectral properties of a chiral random banded matrix (chRBM) with elements decaying as a power-law ${\mathcal{H}}_{ij}\sim |i-j{|}^{-\alpha }$. This model is equivalent to a chiral 1D Anderson Hamiltonian with long range power-law hopping. In the weak disorder limit we obtain explicit nonperturbative analytical results for the density of states and the two-level correlation function by mapping the chRBM onto a nonlinear sigma model. We also put forward, by exploiting the relation between the chRBM at $\alpha =1$ and a generalized chiral random matrix model, an exact expression for the above correlation functions. We give compelling analytical and numerical evidence that for this value the chRBM reproduces all the features of an Anderson transition. Finally we discuss possible applications of our results to QCD.

arXiv comment17 pages, 4 figures; discussions on superconductivity removed

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Cited by in corpus (13)

• Anderson Transitions
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Metal-insulator transition in 2D random fermion systems of chiral symmetry classes
• Poisson to Random Matrix Transition in the QCD Dirac Spectrum
• Chiral phase transition and Anderson localization in the Instanton Liquid Model for QCD
• Boundary multifractality in critical 1D systems with long-range hopping
• Anderson transition in systems with chiral symmetry
• Critical conductance of two-dimensional chiral systems with random magnetic flux
• Spectral statistics of multi-parametric Gaussian ensembles with chiral symmetry
• Extended states with Poisson spectral statistics
• Spectral and Strength Statistics of Chiral Brownian Ensemble
• Transition to chaos in extended systems and their quantum impurity models
• Nonlinear sigma model approach for level correlations in chiral disordered systems