Emergent multifractality in power-law decaying eigenstates

Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality, which is generally believed to be a critical phenomenon and fragile to random perturbations. In this work, we propose a set of generic principles based on the power-law decay of the eigenstates that allow us to distinguish a fractal phase from a genuine multifractal phase. We demonstrate the above principles in a 1D tight-binding model with inhomogeneous nearest-neighbor hopping that can be mapped to the standard quantum harmonic oscillator via energy-coordinate duality. We analytically calculate the fractal dimensions and the spectrum of fractal dimensions, which are in agreement with numerical simulations.