Critical wave-packet dynamics in the power-law bond disordered Anderson Model

TL;DR

This paper studies the critical wave-packet dynamics in a one-dimensional Anderson model with power-law decaying bonds, revealing multifractal eigenstates and distinct scaling regimes in wave-packet spreading.

Contribution

It provides a detailed analysis of wave-packet dynamics at the critical point of a power-law bond disordered Anderson model, including finite-size scaling and multifractality characterization.

Findings

Eigenstates exhibit multifractality with specific fractal dimensions.

Wave-packet spreading shows diffusive-like behavior with power-law tails.

Two distinct scaling regimes observed in participation moments.

Abstract

We investigate the wave-packet dynamics of the power-law bond disordered one-dimensional Anderson model with hopping amplitudes decreasing as $H_{nm}\propto |n-m|^{-\alpha}$. We consider the critical case ($\alpha=1$). Using an exact diagonalization scheme on finite chains, we compute the participation moments of all stationary energy eigenstates as well as the spreading of an initially localized wave-packet. The eigenstates multifractality is characterized by the set of fractal dimensions of the participation moments. The wave-packet shows a diffusive-like spread developing a power-law tail and achieves a stationary non-uniform profile after reflecting at the chain boundaries. As a consequence, the time-dependent participation moments exhibit two distinct scaling regimes. We formulate a finite-size scaling hypothesis for the participation moments relating their scaling exponents to the ones governing the return probability and wave-function power-law decays.