Emergent multifractality in power-law decaying eigenstates

Adway Kumar Das; Anandamohan Ghosh; Ivan M. Khaymovich

doi:10.1103/bnr3-5dcw

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arXiv · 2501.17242

Emergent multifractality in power-law decaying eigenstates

Adway Kumar Das·Anandamohan Ghosh·Ivan M. Khaymovich

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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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Adway Kumar Das, Anandamohan Ghosh, Ivan M. Khaymovich. 2025-01-28. Emergent multifractality in power-law decaying eigenstates. https://doi.org/10.1103/bnr3-5dcw

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