Critical Spectra and Wavefunctions of a One-dimensional Quasiperiodic System

TL;DR

This study explores the spectral and wavefunction properties of a one-dimensional quasiperiodic system derived from a 2D electron lattice in a magnetic field, revealing complex phase transitions and multifractal characteristics.

Contribution

It provides a detailed numerical analysis of the phase diagram, level statistics, and wavefunction scaling in a quasiperiodic system, highlighting novel metallic phase transitions and multifractal behavior.

Findings

Identification of three phases: two metallic and one insulating.

Distinct level statistics distributions near critical points.

Wavefunction scaling exponents consistent with phase diagram.

Abstract

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 $P_B(w)$ near the origin (in the tail) %around the origin (in the tail) have a form $P_B(w) \sim w^{\beta}$ ($P_B(w) \sim e^{-\gamma w}$) ($\beta, \gamma > 0 $), while at the bicritical point $P_B(w) \sim w^{-\beta'}$ ($\beta'>0$). Also distributions of the level spacings follow an inverse power law $P_G(s) \sim s^{- \delta}$ ($\delta > 0$). For the wavefunctions at the centers of spectra, scaling exponents and their distribution in terms of the $\alpha$-$f(\alpha)$-curve are obtained. The results in the vicinity of critical points are consistent with the phase diagram.