Mobility edge and multifractality in a periodically driven Aubry-Andr\'{e} model

TL;DR

This paper investigates the Floquet eigenstates of a driven Aubry-Andre9 model, revealing a unique mobility edge, multifractality, and CAT states, which influence transport and are supported by semi-analytic Floquet Hamiltonian analysis.

Contribution

It introduces the existence of a mobility edge and multifractal states in a driven Aubry-Andre9 model, supported by semi-analytic Floquet Hamiltonian derivation.

Findings

Presence of a mobility edge separating localized and delocalized states.

Observation of multifractal and CAT states in the Floquet spectrum.

Influence of the mobility edge on fermion transport and entropy.

Abstract

We study the localization-delocalization transition of Floquet eigenstates in a driven fermionic chain with an incommensurate Aubry-Andr\'{e} potential and a hopping amplitude which is varied periodically in time. Our analysis shows the presence of a mobility edge separating single-particle delocalized states from localized and multifractal states in the Floquet spectrum. Such a mobility edge does not have any counterpart in the static Aubry-Andr\'{e} model and exists for a range of drive frequencies near the critical frequency at which the transition occurs. The presence of the mobility edge is shown to leave a distinct imprint on fermion transport in the driven chain; it also influences the Shannon entropy and the survival probability of the fermions at long times. In addition, we find the presence of CAT states in the Floquet spectrum with weights centered around a few nearby sites of the chain. This is shown to be tied to the flattening of Floquet bands over a range of quasienergies. We support our numerical studies with a semi-analytic expression for the Floquet Hamiltonian ($H_F$) computed within a Floquet perturbation theory. The eigenspectra of the perturbative $H_F$ so obtained exhibit qualitatively identical properties to the exact eigenstates of $H_F$ obtained numerically. Our results thus constitute an analytic expression of a $H_F$ whose spectrum supports multifractal and CAT states. We suggest experiments which can test our theory.