Publication : t18/121

Abstract:
The nearest-neighbor Aubry-André quasiperiodic localization model is generalized to include power-law translation-invariant hoppings Tl∝t/la or power-law Fourier coefficients Wm∝w/mb in the quasi-periodic potential. The Aubry-André duality between Tl and Wm is manifest when the Hamiltonian is written in the real-space basis and in the Fourier basis on a finite ring. The perturbative analysis in the amplitude t of the hoppings yields that the eigenstates remain power-law localized in real space for a>1 and are critical for ac=1 where they follow the Strong Multifractality linear spectrum, as in the equivalent model with random disorder. The perturbative analysis in the amplitude w of the quasi-periodic potential yields that the eigenstates remain delocalized in real space (power-law localized in Fourier space) for b>1 and are critical for bc=1 where they follow the Weak Multifractality gaussian spectrum in real space (or Strong Multifractality linear spectrum in the Fourier basis). This critical case bc=1 for the Fourier coefficients Wm corresponds to a periodic function with discontinuities, instead of the cosinus of the standard self-dual Aubry-André model.

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