Emergent multifractality in power-law decaying eigenstates

• URL: http://arxiv.org/abs/2501.17242v1
• Date: Tue, 28 Jan 2025 19:01:40 GMT
• Title: Emergent multifractality in power-law decaying eigenstates
• Authors: Adway Kumar Das, Anandamohan Ghosh, Ivan M. Khaymovich,
• Abstract summary: Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. We propose a set of generic principles based on the power-law decay of the eigenstates which allow us to distinguish a fractal phase from a genuine multifractal phase. We analytically calculate the fractal dimensions and the spectrum of fractal dimensions which are in agreement with numerical simulations.
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• Abstract: 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 which 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.

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