Multifractality of quantum wave functions in the presence of perturbations

TL;DR

This paper investigates how quantum multifractality is affected by various perturbations across different models, providing analytical and numerical insights to guide experimental observation of multifractal phenomena.

Contribution

It offers a comprehensive analysis of multifractality destruction mechanisms under perturbations, including analytical theories and large-scale simulations across multiple models.

Findings

Multifractality can be preserved below a characteristic length scale.

Strong perturbations can cause uniform disappearance of multifractality.

Subtle variants of destruction scenarios exist depending on the model and perturbation.

Abstract

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model and a random matrix model. We apply several types of natural perturbations which can be relevant for experimental implementations. We construct an analytical theory for certain cases, and perform extensive large-scale numerical simulations in other cases. The data are analyzed through refined methods including double scaling analysis. Our results confirm the recent conjecture that multifractality breaks down following two scenarios. In the first one, multifractality is preserved unchanged below a certain characteristic length which decreases with perturbation strength. In the second one, multifractality is affected at all scales and disappears uniformly for a strong enough perturbation. Our refined analysis shows that subtle variants of these scenarios can be present in certain cases. This study could guide experimental implementations in order to observe quantum multifractality in real systems.