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<p>Eigenstate multifractality, a hallmark of non-interacting disordered metals, features anomalously slow dynamics and is relevant across quantum platforms ranging from measurement-driven systems to superconductivity. Despite extensive work on multifractality in disordered and quasiperiodic systems, deterministic, disorder-free lattice routes remain underexplored. Here, we demonstrate non-ergodic multifractal states (NEMs) by iteratively placing defects to shape a crystal lattice into a fractal geometry. Through a comprehensive analysis of the Sierpiński gasket, we find consistent evidence for the emergence of NEMs that go beyond the conventional classification of quantum states and open new pathways for quantum transport studies. We further outline experimental signatures of these states.</p>

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Emergence of non-ergodic multifractal quantum states in geometric fractals

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年1月8日

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  • Fabio Salvati,
  • Mikhail I. Katsnelson,
  • Andrey A. Bagrov

摘要

Eigenstate multifractality, a hallmark of non-interacting disordered metals, features anomalously slow dynamics and is relevant across quantum platforms ranging from measurement-driven systems to superconductivity. Despite extensive work on multifractality in disordered and quasiperiodic systems, deterministic, disorder-free lattice routes remain underexplored. Here, we demonstrate non-ergodic multifractal states (NEMs) by iteratively placing defects to shape a crystal lattice into a fractal geometry. Through a comprehensive analysis of the Sierpiński gasket, we find consistent evidence for the emergence of NEMs that go beyond the conventional classification of quantum states and open new pathways for quantum transport studies. We further outline experimental signatures of these states.