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

Understand

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.