Study of localization properties under subsystem periodic driving

Abstract

Periodic driving provides a powerful route for controlling localization and engineering effective Hamiltonians in quantum systems. A localized one-dimensional Aubry-André chain can be driven into a fully delocalized phase when the entire system is driven below a critical frequency. Here, we ask whether such delocalization can be achieved by driving only a part of the system. We address this question using a two-leg ladder comprising an Aubry-André chain coupled to a periodically driven clean tight-binding chain. Exact numerical calculations show that, starting from a localized static ladder, subsystem driving below a critical frequency cannot achieve complete delocalization. Instead, a mixed phase emerges, with localized and delocalized states coexisting and the fraction of delocalized states varying nonmonotonically with the driving frequency. This behavior can be understood using local effective Hamiltonians. Although these effective Hamiltonians are derived analytically in the high-frequency regime, they can nevertheless predict the localization transition occurring in the moderate-frequency regime. In fact, by quantifying the emergent nonlocality of the Floquet Hamiltonian, we show that these effective Hamiltonians provide a valid description up to a crossover frequency that is lower than the critical frequency associated with the localization transition. Our results demonstrate an alternative route to Floquet engineering, in which the transport properties of a quantum lattice system can be modified by driving only a subsystem.

Can periodic driving restricted to one subsystem delocalize an otherwise localized composite lattice? This paper studies a noninteracting two-leg ladder comprising a clean tight-binding chain coupled to an Aubry–André chain, with a spatially uniform square-wave onsite potential applied only to the clean leg. The analysis combines exact single-particle Floquet diagonalization, participation-ratio finite-size comparisons, and rotating-frame and van Vleck effective Hamiltonians. For intraleg hopping $t_A=t_B=1$, rung coupling $t'=10$, quasiperiodic potential $V_B=6$, and drive amplitude $V_A=20$, the initially localized ladder develops coexisting localized and extended states below approximately $\omega_c=17$, rather than becoming fully extended. The inferred extended fraction varies nonmonotonically with frequency. Sorted-IPR comparisons use total sizes up to $2N=1500$; the quantitative fraction uses sizes 500 and 1000 and a specified size-dependence threshold. The leading rotating-frame description retains a local ladder with effective rung hopping $t'_{\mathrm{eff}}=t'\,\mathrm{sinc}(\pi V_A/2\omega)$. It approximately reproduces the localization-transition frequency. Distance-resolved matrix elements of the exact Floquet Hamiltonian indicate appreciable longer-range interleg couplings below a crossover near $\omega_{\mathrm{cr}}\simeq15$, below the localization transition. The effective descriptions are controlled at high frequency and deviate at lower frequencies; their predicted suppression of rung hopping does not establish exact dynamical decoupling. The reported phase classification relies on finite-size scaling criteria. Interactions, heating, additional ladder legs, and broader driving protocols remain outside the study.