# Multifractality without fine-tuning in a Floquet quasiperiodic chain

## TL;DR

This paper demonstrates the emergence of robust multifractal wavefunctions in a driven quasiperiodic quantum chain, which do not require fine-tuning and could have implications for quantum applications.

## Contribution

It reveals a new form of multifractality in Floquet systems that is inherently robust and arises without fine-tuning, supported by a simple theoretical model.

## Key findings

- Multifractality appears in a driven quasiperiodic chain without fine-tuning.
- The phenomenon is explained by a random matrix theory model.
- Potential experimental signatures in cold atom systems are discussed.

## Abstract

Periodically driven, or Floquet, disordered quantum systems have generated many unexpected discoveries of late, such as the anomalous Floquet Anderson insulator and the discrete time crystal. Here, we report the emergence of an entire band of multifractal wavefunctions in a periodically driven chain of non-interacting particles subject to spatially quasiperiodic disorder. Remarkably, this multifractality is robust in that it does not require any fine-tuning of the model parameters, which sets it apart from the known multifractality of $critical$ wavefunctions. The multifractality arises as the periodic drive hybridises the localised and delocalised sectors of the undriven spectrum. We account for this phenomenon in a simple random matrix based theory. Finally, we discuss dynamical signatures of the multifractal states, which should betray their presence in cold atom experiments. Such a simple yet robust realisation of multifractality could advance this so far elusive phenomenon towards applications, such as the proposed disorder-induced enhancement of a superfluid transition.