SciPost Physics

SciPost Phys. 16, 008 (2024) · published 9 January 2024

• doi: 10.21468/SciPostPhys.16.1.008
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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 Rosenzweig-Porter (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.

• Vanoni et al., Analysis of localization transitions using nonparametric unsupervised learning
  Phys. Rev. B 110, 024204 (2024) [Crossref]
• Buijsman, Long-range spectral statistics of the Rosenzweig-Porter model
  Phys. Rev. B 109, 024205 (2024) [Crossref]
• Čadež et al., The Rosenzweig–Porter model revisited for the three Wigner–Dyson symmetry classes
  New J. Phys. 26, 083018 (2024) [Crossref]
• Cugliandolo et al., Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
  Phys. Rev. B 110, 174202 (2024) [Crossref]