Signatures of multifractality in a periodically driven interacting Aubry-Andr\'{e} model

TL;DR

This paper investigates the transition from ergodic to many-body localized phases in a driven interacting fermionic chain with an incommensurate potential, revealing multifractal eigenstates at intermediate drive frequencies and proposing experimental detection methods.

Contribution

It uncovers the existence of multifractal Floquet eigenstates in a driven Aubry-André model and analyzes their signatures through various physical observables, supported by semi-analytic Floquet theory.

Findings

Transition from ergodic to Floquet-MBL with increasing drive frequency

Existence of a multifractal phase characterized by non-trivial fractal dimensions

Distinct auto-correlation and transport signatures in the multifractal regime

Abstract

We study the many-body localization (MBL) transition of Floquet eigenstates in a driven, interacting fermionic chain with an incommensurate Aubry-Andr\'{e} potential and a time-periodic hopping amplitude as a function of the drive frequency $\omega_D$ using exact diagonalization (ED). We find that the nature of the Floquet eigenstates change from ergodic to Floquet-MBL with increasing frequency; moreover, for a significant range of intermediate $\omega_D$, the Floquet eigenstates exhibit non-trivial fractal dimensions. We find a possible transition from the ergodic to this multifractal phase followed by a gradual crossover to the MBL phase as the drive frequency is increased. We also study the fermion auto-correlation function, entanglement entropy, normalized participation ratio (NPR), fermion transport and the inverse participation ratio (IPR) as a function of $\omega_D$. We show that the auto-correlation, fermion transport and NPR displays qualitatively different characteristics (compared to their behavior in the ergodic and MBL regions) for the range of $\omega_D$ which supports multifractal eigenstates. In contrast, the entanglement growth in this frequency range tend to have similar features as in the MBL regime; its rate of growth is controlled by $\omega_D$. Our analysis thus indicates that the multifractal nature of Floquet-MBL eigenstates can be detected by studying auto-correlation function and fermionic transport of these driven chains. We support our numerical results with a semi-analytic expression of the Floquet Hamiltonian obtained using Floquet perturbation theory (FPT) and discuss possible experiments which can test our predictions.