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

Abstract

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 study, we present analytical evidence, supported by exact numerical computations, that demonstrates the controllable tuning of the phase diagram in the RP model by employing on-site potentials with a non-trivial fractal dimension instead of the conventional random disorder. We demonstrate that doing so extends the fractal phase and creates unusual dependence of fractal dimensions of the eigenfunctions. Furthermore, we study the fate of level statistics in such a system and analyze the return probability of a wave packet localized at a single site to provide a dynamical test-bed for our theory.

5 pages, 5 figures, 65 references + 3 pages, 2 figures in Appendices

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Cited by in corpus (15)

• Anatomy of the eigenstates distribution: a quest for a genuine multifractality
• The Rosenzweig Porter model revisited for the three Wigner Dyson symmetry classes
• Long-range spectral statistics of the Rosenzweig-Porter model
• Emergent multifractality in power-law decaying eigenstates
• Critical dynamics of long-range quantum disordered systems
• Re-entrant localization induced by short-range hopping in the fractal Rosenzweig-Porter Model
• Spectral form factor and energy correlations in banded random matrices
• Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
• Quantum logarithmic multifractality
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• The Wishart--Rosenzweig--Porter random matrix ensemble
• Spectral statistics and energy-gap scaling in $k-$local spin Hamiltonians
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder