# From ergodic to non-ergodic chaos in Rosenzweig-Porter model

## TL;DR

This paper investigates the phase transitions in the Rosenzweig-Porter model, revealing that non-ergodic chaotic and ergodic regimes are separated by a continuous transition, characterized through numerical analysis of key quantities.

## Contribution

It provides a numerical characterization of the phases and transitions in the Rosenzweig-Porter model, highlighting the continuous nature of the non-ergodic to ergodic transition.

## Key findings

- Identification of three phases: ergodic, non-ergodic extended, localized
- Numerical evidence of non-analytical behavior in key quantities
- Continuous phase transition between non-ergodic chaotic and ergodic regimes

## Abstract

The Rosenzweig-Porter model is a one-parameter family of random matrices with three different phases: ergodic, extended non-ergodic and localized. We characterize numerically each of these phases and the transitions between them. We focus on several quantities that exhibit non-analytical behaviour and show that they obey the scaling hypothesis. Based on this, we argue that non-ergodic chaotic and ergodic regimes are separated by a continuous phase transition, similarly to the transition between non-ergodic chaotic and localized phases.