Multifractality of Hamiltonians with power-law transfer terms

TL;DR

This paper numerically investigates finite-size effects on generalized fractal dimensions in a 1D disordered model with power-law transfer terms, revealing linear dependence of $d_q$ on $q$ in different coupling regimes.

Contribution

It provides new numerical insights into the multifractality of Hamiltonians with power-law transfer terms across different coupling regimes.

Findings

Linear dependence of $d_q$ on $q$ for $q extless 4g^{-1}$

Finite-size effects significantly influence fractal dimensions

Multifractality persists in both strong and weak coupling regimes

Abstract

Finite-size effects in the generalized fractal dimensions $d_q$ are investigated numerically. We concentrate on a one-dimensional disordered model with long-range random hopping amplitudes in both the strong- and the weak-coupling regime. At the macroscopic limit, a linear dependence of $d_q$ on $q$ is found in both regimes for values of $q \alt 4g^{-1}$, where $g$ is the coupling constant of the model.