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  • Letter
  • Open Access

Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder

Madhumita Sarkar*

Roopayan Ghosh

Ivan M. Khaymovich

  • Jožef Stefan Institute, SI-1000 Ljubljana, Slovenia

  • Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom

  • Nordita, Stockholm University and KTH Royal Institute of Technology Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden and Institute for Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, GSP-105, Russia

  • *sarkar.madhumita770@gmail.com
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Phys. Rev. B 108, L060203 – Published 29 August, 2023

DOI: https://doi.org/10.1103/PhysRevB.108.L060203

Abstract

The Rosenzweig-Porter (RP) model has garnered much attention in the last decade, as it is a simple analytically tractable model showing both ergodic-nonergodic extended and Anderson localization transitions. Thus, it is a good toy model to understand the Hilbert-space structure of many-body localization phenomenon. In our Letter, we present analytical evidence, supported by exact numerics, that demonstrates the controllable tuning of the phase diagram in the RP model by employing on-site potentials with a nontrivial fractal dimension instead of the conventional random disorder. We demonstrate that such disorder extends the fractal phase and creates an unusual dependence of fractal dimensions of the eigenfunctions. Furthermore, we study the fate of level statistics in such a system to understand how these changes are reflected in the eigenvalue statistics.

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Phys. Rev. B 108, L060203– Published 29 August, 2023
  • Received 6 June 2023
  • Accepted 10 August 2023
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