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Anatomy of the eigenstates distribution: a quest for a genuine multifractality
by Anton Kutlin, Ivan M. Khaymovich
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Submission summary
| Authors (as registered SciPost users): | Ivan Khaymovich · Anton Kutlin |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2309.06468v2 (pdf) |
| Date accepted: | 2023-12-21 |
| Date submitted: | 2023-12-13 18:01 |
| Submitted by: | Kutlin, Anton |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Motivated by a series of recent works, an interest in multifractal phases has risen as they are believed to be present in the Many-Body Localized (MBL) phase and are of high demand in quantum annealing and machine learning. Inspired by the success of the RosenzweigPorter (RP) model with Gaussian-distributed hopping elements, several RP-like ensembles with the fat-tailed distributed hopping terms have been proposed, with claims that they host the desired multifractal phase. In the present work, we develop a general (graphical) approach allowing a self-consistent analytical calculation of fractal dimensions for a generic RP model and investigate what features of the RP Hamiltonians can be responsible for the multifractal phase emergence. We conclude that the only feature contributing to a genuine multifractality is the on-site energies' distribution, meaning that no random matrix model with a statistically homogeneous distribution of diagonal disorder and uncorrelated off-diagonal terms can host a multifractal phase.
List of changes
Due to the request of Referee #1:
1. The explanation of the discrepancy between the results of the present paper and the paper [31] ([29] in the previous version) is added to the end of Sec.5
2. The notion of the running exponent and the meaning of the power law tails in PDFs of fractal distributions are clarified in the introduction.
3. The reference to "The large deviation approach to statistical mechanics" by H. Touchette is added, and the relation of our theory to the large deviation theory is discussed at the end of Sec.2
4. Above Eq. (22): the world order was changed to clarify the meaning of the "broadening typical value."
5. Below Eq. (37): the "eaten by the extensive number" slang was corrected.
6. Below Fig. 7, especially the paragraph starting from "The reason why...": the end of Sec. 5 was significantly rewritten to clarify several important points.
7. On p. 16, below Fig. 7, and in other places, the misprint was corrected, and "providing" was replaced with "provided."
8. Fig. 8 was updated, and its caption was extended to make it more accessible.
9. Below Eq. (48): "multifractality" was replaced with "multifractal."
10. We have extended the description of which part of the phase diagram we have meant after Eq. (48) and in the caption of Fig. 10.
11. We replaced "let's" with "let us" and "haven't" with "have not."
Due to the review from Referee #2, we have added a discussion of possible method generalizations to the conclusion.
Published as SciPost Phys. 16, 008 (2024)