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

Fuente: arXiv
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Main Authors: Kutlin, Anton, Khaymovich, Ivan M.
Format: Preprint
Published: 2023
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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
id 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