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Emergent multifractality in power-law decaying eigenstates

Adway Kumar Das* and Anandamohan Ghosh†

Ivan M. Khaymovich‡

  • *Contact author: akd19rs062@iiserkol.ac.in
  • †Contact author: anandamohan@iiserkol.ac.in
  • ‡Contact author: ivan.khaymovich@gmail.com
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Phys. Rev. B 112, 024201 – Published 1 July, 2025

DOI: https://doi.org/10.1103/bnr3-5dcw

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 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.

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Phys. Rev. B 112, 024201– Published 1 July, 2025
  • Received 4 February 2025
  • Revised 17 June 2025
  • Accepted 18 June 2025
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