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

Viktor Z. Cerovski
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Abstract

Bond-disordered Anderson model in two dimensions on a square lattice is studied numerically near the band center by calculating density of states (DoS), multifractal properties of eigenstates and the localization length. DoS divergence at the band center is studied and compared with Gade's result [Nucl. Phys. B 398, 499 (1993)] and the powerlaw. Although Gade's form describes accurately DoS of finite size systems near the band-center, it fails to describe the calculated part of DoS of the infinite system, and a new expression is proposed. Study of the level spacing distributions reveals that the state closest to the band center and the next one have different level spacing distribution than the pairs of states away from the band center. Multifractal properties of finite systems furthermore show that scaling of eigenstates changes discontinuously near the band center. This unusual behavior suggests the existence of a new 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 scaling of Lyapunov exponents of transfer matrices of long stripes indicates that for a long stripe of any width there is an energy region around band center within which the Lyapunov exponents cannot be described by one-parameter scaling. This region, however, vanishes in the limit of the infinite square lattice when one-parameter scaling is restored, and the scaling exponent calculated, in agreement with the result of the finite size scaling analysis.

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Viktor Z. Cerovski. 2000-08-21. Bond-disordered Anderson model on a two dimensional square lattice - chiral symmetry and restoration of one-parameter scaling. https://doi.org/10.1103/physrevb.62.12775

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