Bounding multifractality by observables

• URL: http://arxiv.org/abs/2501.17649v1
• Date: Wed, 29 Jan 2025 13:29:20 GMT
• Title: Bounding multifractality by observables
• Authors: Tuomas I. Vanhala, Niklas Järvelin, Teemu Ojanen,
• Abstract summary: Fractal dimensions have been used as a measure for structure of eigenstates of quantum many-body systems. We discuss how this structure of the observables can be used to bound the fractal dimensions from above. We then consider how such upper bounds act as a proxy for the fractal dimension over the many-body localization transition.
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• Abstract: Fractal dimensions have been used as a quantitative measure for structure of eigenstates of quantum many-body systems, useful for comparison to random matrix theory predictions or to distinguish many-body localized systems from chaotic ones. For chaotic systems at midspectrum the states are expected to be ``ergodic'', infinite temperature states with all fractal dimensions approaching 1 in the thermodynamic limit. However, when moving away from midspectrum, the states develop structure, as they are expected to follow the eigenstate thermalization hypothesis, with few-body observables predicted by a finite-temperature ensemble. We discuss how this structure of the observables can be used to bound the fractal dimensions from above, thus explaining their typical arc-shape over the energy spectrum. We then consider how such upper bounds act as a proxy for the fractal dimension over the many-body localization transition, thus formally connecting the single-particle and Fock space pictures discussed in the literature.

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