Bond-disordered Anderson model on a two-dimensional square lattice: Chiral symmetry and restoration of one-parameter scaling

Abstract

The bond-disordered Anderson model in two dimensions on a square lattice is studied numerically near the band center by calculating the density of states (DOS), multifractal properties of eigenstates, and the localization length. The DOS divergence at the band center is studied and compared with Gade's result and power law. Although Gade's form describes accurately the DOS of finite-size systems near the band center, it fails to describe the calculated part of the DOS of the infinite system, and a different expression is proposed. Study of the level spacing distributions reveals that the state closest to the band center and the next one have a different level spacing distribution than pairs of states away from the band center. Multifractal properties of finite systems furthermore show that the scaling of eigenstates changes discontinuously near the band center. This unusual behavior suggests the existence of a divergent length scale, whose existence is explained as the finite-size manifestation of the band center critical point of the infinite system, and the critical exponent of the correlation length is calculated by a finite-size scaling. Furthermore, study of the scaling of the Lyapunov exponents of transfer matrices of long stripes indicates that for a long stripe of any width there is an energy region around the band center within which the Lyapunov exponents cannot be described by one-parameter scaling. This region vanishes, however, in the limit of the infinite square lattice, when one-parameter scaling is restored, and the scaling exponent calculated is in agreement with the result of the finite-size scaling analysis.