Emergent multifractality in power-law decaying eigenstates

TL;DR

This paper introduces generic principles based on power-law decay of eigenstates to distinguish fractal from multifractal phases, demonstrated through analytical and numerical analysis of a 1D model.

Contribution

It proposes a universal framework for identifying multifractality in eigenstates, moving beyond fine-tuned models and critical phenomena.

Findings

Analytical calculation of fractal dimensions matches numerical results.

Distinction between fractal and multifractal phases established.

Model mapped to quantum harmonic oscillator for analysis.

Abstract

Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality which is generally believed to be a critical phenomenon and fragile to random perturbations. In this work, we propose a set of generic principles based on the power-law decay of the eigenstates which allow us to distinguish a fractal phase from a genuine multifractal phase. We demonstrate the above principles in a 1d tight-binding model with inhomogeneous nearest-neighbor hopping that can be mapped to the standard quantum harmonic oscillator via energy-coordinate duality. We analytically calculate the fractal dimensions and the spectrum of fractal dimensions which are in agreement with numerical simulations.