Critical generalized inverse participation ratio distributions

Article

关键词: 2 DIMENSIONS;    SPECTRAL STATISTICS;    ANDERSON TRANSITION;    DISORDERED-SYSTEMS;    MAGNETIC-FIELD;    LOCALIZATION;    EIGENFUNCTIONS;    FLUCTUATIONS;    MULTIFRACTALITY;    METALS;   

DOI  :  10.1103/PhysRevB.66.233103

来源: SCIE

【 摘 要 】

The system size dependence of the fluctuations in generalized inverse participation ratios (IPR's) I-alpha(q) at criticality is investigated numerically. We focus on a three-dimensional (3D) system with unitary symmetry, a 2D system with symplectic symmetry and a 1D system with orthogonal symmetry. The variances of the IPR logarithms are found to be scale-invariant at the macroscopic limit. The finite size corrections to the variances decay algebraically with nontrivial exponents, which depend on the Hamiltonian symmetry and the dimensionality. The large-q dependence of the asymptotic values of the variances behaves as q(2) according to theoretical estimates. These results ensure the self-averaging of the corresponding generalized dimensions.

【 授权许可】

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