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.

17 pages, 4 figures; discussions on superconductivity removed

Cited by in corpus (6)

• Anderson Transitions
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Boundary multifractality in critical 1D systems with long-range hopping
• Anderson transition in systems with chiral symmetry
• Transition to chaos in extended systems and their quantum impurity models
• Nonlinear sigma model approach for level correlations in chiral disordered systems