Anatomy of the eigenstates distribution: a quest for a genuine multifractality

• URL: http://arxiv.org/abs/2309.06468v2
• Date: Tue, 12 Dec 2023 16:53:19 GMT
• Title: Anatomy of the eigenstates distribution: a quest for a genuine multifractality
• Authors: Anton Kutlin and Ivan M. Khaymovich
• Abstract summary: Interest in multifractal phases has risen as they are believed to be present in the Many-Body Localized (MBL) phase. Several RP-like ensembles with the fat-tailed distributed hopping terms have been proposed, with claims that they host the desired multifractal phase.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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