Geometry Induced Localization and Multifractality in Spiral quasiperiodic chain

TL;DR

This paper investigates how spiral geometry influences localization and multifractality in a quasiperiodic Aubry-Andre lattice, revealing geometry-induced effects on wavefunction behavior and potential applications in various physical platforms.

Contribution

It demonstrates that spiral geometry significantly enhances localization and multifractality in quasiperiodic systems, a novel insight into geometry-wavefunction interactions.

Findings

Curvature promotes localization at lower quasiperiodic strengths.

Eigenstates exhibit strong multifractality in certain parameter windows.

States evolve smoothly from extended to localized with increasing quasiperiodicity.

Abstract

We study a quasiperiodic Aubry Andre lattice arranged along a spiral curve. In this setup, the changing angle of the spiral naturally stretches and compresses the distances between neighboring sites, which in turn modulates the hopping amplitudes. The onsite potential itself remains the familiar AA form, but this geometry induced variation in the hopping dramatically changes how the system behaves both in its energy spectrum and in how its states localize.Using inverse participation ratios together with a full multifractal analysis, we find that curvature makes the system localize much more easily, even at relatively small quasiperiodic strengths. It also produces clear windows where the eigenstates become strongly multifractal. This shows that quasiperiodicity and geometry do not act independently rather, they reinforce one another in shaping the wavefunctions. Overall, we observe a smooth evolution of the states from extended, to multifractal, and finally to strongly localized. Our results pave the way for creating tunable quasiperiodic and geometry-driven localization effects in photonic waveguide arrays, ultracold atoms, mechanical metamaterials, and nanoscale platforms.