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

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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Cited by in corpus (10)

• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• Long-range spectral statistics of the Rosenzweig-Porter model
• The Rosenzweig Porter model revisited for the three Wigner Dyson symmetry classes
• An analysis of localization transitions using non-parametric unsupervised learning
• Emergent multifractality in power-law decaying eigenstates
• Investigating finite-size effects in random matrices by counting resonances
• Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
• Local Density of States Correlations in the Lévy-Rosenzweig-Porter random matrix ensemble
• Classes of non-Gaussian random matrices: long-range eigenvalue correlations and non-ergodic extended eigenvectors
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians