2005/12/22 by Kazusumi Ino, Ino, Kazusumi, Mahito Kohmoto +1
Materials Science · Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Liquid Crystal Research Advancements #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.cond-mat/0512562
RevTex, 21 pages,23 figures
arxiv created 2005/12/22 · openalex publication_date 2005/12/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We numerically study a one dimensional quasiperiodic system obtained from two dimensional electrons on the triangular lattice in a uniform magnetic field aided by the multifractal method. The phase diagram consists of three phases: two metallic phases and one insulating phase separated by critical lines with one bicritical point. Novel transitions between the two metallic phases exist. We examine the spectra and the wavefunctions along the critical lines. Several types of level statistics are obtained. Distributions of the band widths PB(w) near the origin (in the tail) %around the origin (in the tail) have a form PB(w) ∼ wβ (PB(w) ∼ e-γw) (β, γ> 0 ), while at the bicritical point PB(w) ∼ w-β' (β'>0). Also distributions of the level spacings follow an inverse power law PG(s) ∼ s- δ (δ> 0). For the wavefunctions at the centers of spectra, scaling exponents and their distribution in terms of the α-f(α)-curve are obtained. The results in the vicinity of critical points are consistent with the phase diagram.