Anatomy of the eigenstates distribution: a quest for a genuine multifractality
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911758792261632 |
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| author | Kutlin, Anton Khaymovich, Ivan M. |
| author_facet | Kutlin, Anton Khaymovich, Ivan M. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_06468 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Anatomy of the eigenstates distribution: a quest for a genuine multifractality Kutlin, Anton Khaymovich, Ivan M. Disordered Systems and Neural Networks Statistical Mechanics Data Analysis, Statistics and Probability Quantum Physics 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. |
| title | Anatomy of the eigenstates distribution: a quest for a genuine multifractality |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Data Analysis, Statistics and Probability Quantum Physics |
| url | https://arxiv.org/abs/2309.06468 |