Periodically driven model with quasiperiodic potential and staggered hopping amplitudes: engineering of mobility gaps and multifractal states

TL;DR

This paper explores how periodic driving in a quasiperiodic Aubry-Andre9 model creates novel Floquet phases with mobility gaps and multifractal states, revealing complex phase transitions and extended states not present in the static system.

Contribution

It introduces a driven quasiperiodic model exhibiting four distinct phases, including multifractal states and mobility gaps, expanding understanding of Floquet phases beyond static models.

Findings

Four phases identified: extended, localized, multifractal, and mixed states.

Re-entrant transitions occur when varying frequency and potential strength.

High-frequency limit yields static-like quasienergies but more extended eigenstates.

Abstract

We study if periodic driving of a model with a quasiperiodic potential can generate interesting Floquet phases which have no counterparts in the static model. Specifically, we consider the Aubry-Andr\'e model which is a one-dimensional time-independent model with an on-site quasiperiodic potential $V_0$ and a nearest-neighbor hopping amplitude which is taken to have a staggered form. We add a uniform hopping amplitude which varies periodically in time with a frequency $\omega$. Unlike the static Aubry-Andr\'e model which has a simple phase diagram with only two phases (only extended or only localized states), we find that the driven model has four possible phases: a phase with only extended states, a phase with multiple mobility gaps separating different quasienergy bands, a mixed phase with coexisting extended, multifractal, and localized states, and a phase with only localized states. The multifractal states have generalized inverse participation ratios which scale with the system size with exponents which are different from the values for both extended and localized states. In addition, we observe intricate re-entrant transitions between the different kinds of states when $\omega$ and $V_0$ are varied. In the limit of high frequency and large driving amplitude, we find that the Floquet quasienergies match the energies of the undriven system, but the Floquet eigenstates are much more extended. We also study the spreading of a one-particle wave packet and find that it is always ballistic but the ballistic velocity varies significantly with the system parameters, sometimes showing a non-monotonic dependence on $V_0$ which does not occur in the static model. We conclude that the interplay of quasiperiodic potential and driving produces a rich phase diagram which does not appear in the static model.