On super-Poissonian behavior of the Rosenzweig-Porter model in the non-ergodic extended regime

TL;DR

This paper investigates the spectral properties of the Rosenzweig-Porter model in the non-ergodic extended phase, providing evidence for super-Poissonian statistics and correlated mini-bands through spectral analysis methods.

Contribution

It offers new spectral evidence for correlated mini-bands and super-Poissonian behavior in the non-ergodic extended regime of the Rosenzweig-Porter model, using novel analysis techniques.

Findings

Spectral rigidity results are inconclusive due to Thouless energy issues.

Singular value decomposition reveals super-Poissonian spectral statistics.

Evidence supports the existence of correlated mini-bands in the spectrum.

Abstract

The Rosenzweig-Porter model has seen a resurgence in interest as it exhibits a non-ergodic extended phase between the ergodic extended metallic phase and the localized phase. Such a phase is relevant to many physical models from the Sachdev-Ye-Kitaev model in high-energy physics and quantum gravity, to the interacting many-body localization in condensed matter physics and quantum computing. This phase is characterized by fractal behavior of the wavefunctions, and a postulated correlated mini-band structure of the energy spectrum. Here we will seek evidence for the latter in the spectrum. Since this behavior is expected on intermediate energy scales spectral rigidity is a natural way to tease it out. Nevertheless, due to the Thouless energy and ambiguities in the unfolding procedure, the results are inconclusive. On the other hand, by using the singular value decomposition method, clear evidence for a super-Poissonian behavior in this regime emerges, consistent with a picture of correlated mini-bands.