From pink to brown: Interaction-driven noise color shift in the Aubry-André Model
We revisit the metal-insulator transition in a one-dimensional lattice subjected to an on-site quasiperiodic potential, modeled using spin-1/2 particles with tunable nearest-neighbor interactions. To characterize the transition, we examine the power-spectrum, defined as the squared modulus of the Fourier transform of consecutive level spacings. In the absence of interactions, the power-spectrum fails to capture clear signatures of the transition, consistently exhibiting brown-noise-like behavior across regimes. In contrast, the interacting case reveals a marked change: the metallic phase displays spectral fluctuations consistent with pink noise, while the insulating phase is characterized by brown noise. These results are supported by analyses of the level spacing distribution and the level number variance. Additionally, we demonstrate that both statistics and the structure of energy eigenstates provide reliable indicators of the transition, in both interacting and non-interacting scenarios.