Emergence of criticality through a cascade of delocalization transitions in quasiperiodic chains

Abstract

Conduction through materials crucially depends on how ordered they are. Periodically ordered systems exhibit extended Bloch waves that generate metallic bands, whereas disorder is known to limit conduction and localize the motion of particles in a medium. In this context, quasiperiodic systems, which are neither periodic nor disordered, reveal exotic conduction properties, self-similar wavefunctions, and critical phenomena. Here, we explore the localization properties of waves in a novel family of quasiperiodic chains obtained when continuously interpolating between two paradigmatic limits: the Aubry-André model, famous for its metal-to-insulator transition, and the Fibonacci chain, known for its critical nature. Using both theoretical analysis and experiments on cavity-polariton devices, we discover that the Aubry-André model evolves into criticality through a cascade of band-selective localization/delocalization transitions that iteratively shape the self-similar critical wavefunctions of the Fibonacci chain. Our findings offer (i) a unique new insight into understanding the criticality of quasiperiodic chains, (ii) a controllable knob by which to engineer band-selective pass filters, and (iii) a versatile experimental platform with which to further study the interplay of many-body interactions and dissipation in a wide range of quasiperiodic models.

arXiv comment7 pages, 4 figures + supplementary material (9 pages, 6 figures, 2 videos), comments are welcome

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• Critical and Topological Phases of Dimerized Kitaev Chain in Presence of Quasiperiodic Potential
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• Observation of Light Localization at the Edges of Quasicrystal Waveguide Arrays
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• Multifractal Properties of Tribonacci Chains
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