Fig. 4: Energy gaps distribution.
Integrated level spacing distribution pint(s) for the energy spectra on different lattices: Solid lines are for triangular geometries, with the fractal Sierpiński gasket (SG) of generation 7 (3282 sites) in blue, the corresponding regular triangular lattice (RTL) with 8385 sites in red, and the Sierpiński gasket used in experiment3 in green (SG exp.) The dash-dotted lines correspond to square geometries, where the blue is the fractal Sierpiński carpet (SC) of generation 5 (5280 sites), and the red one is the regular square lattice (RSqL) with the same basis (6724 sites). Only on the gasket (SG and SG exp), the integrated level spacing distribution exhibits approximately an inverse power-law behavior pint(s) ~ s1−β. This allows to determine the exponent β via fitting, β ≈ 1.60 ± 0.05 for SG, and β ≈ 2.25 ± 0.05 for SG exp.
