Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain

Abstract

In this paper, we explore the localization features of wave functions in a family of mosaic quasiperiodic chains obtained by continuously interpolating between two limits: the mosaic Aubry-André (AA) model, known for its exact mobility edges with extended states in the band-center region, and localized ones in the band-edge regions for a large enough modulation amplitude, and the mosaic Fibonacci chain, which exhibits its multifractal nature for all the states except for the extended one with $E=0$ for an arbitrary finite modulation amplitude. We discover that the mosaic AA limit for the states in the band-edge regions evolves into multifractal ones through a cascade of delocalization transitions. This cascade shows lobes of lower fractal dimension values separated by maxima of fractal dimension. In contrast, the states in the band-center region (except for the $E=0$ state) display an anomalous cascading process, where it emerges lobes of higher fractal dimension values are separated by the regions with lower fractal dimensions. Our findings offer insight into understanding the multifractality of quasiperiodic chains.

12 pages, 11 figures

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Cited by in corpus (13)

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• The fundamental localization phases in quasiperiodic systems: A unified framework and exact results
• Multiple intermediate phases in the interpolating Aubry-André-Fibonacci model
• Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays
• Fibonacci-Modulation-Induced Multiple Topological Anderson Insulators
• Resonances, mobility edges and gap-protected Anderson localization in generalized disordered mosaic lattices
• Stability of quasicrystalline ultracold fermions to dipolar interactions
• Fate of localization features in a one-dimensional non-Hermitian flat-band lattice with quasiperiodic modulations
• Exact mobility edges in quasiperiodic network models with slowly varying potentials
• Types of dynamical behavior in a quasiperiodic mosaic lattice
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Two-strand ladder network variants: localization, multifractality, and quantum dynamics under an Aubry-André-Harper kind of quasiperiodicity
• Exact mobility edges in a slowly varying quasiperiodic ladder model