Circular Rosenzweig-Porter random matrix ensemble

TL;DR

This paper introduces a circular analogue of the Rosenzweig-Porter random matrix ensemble to model the spectral and eigenstate properties of periodically driven many-body localized systems, supported by numerical evidence.

Contribution

It proposes a new unitary (circular) ensemble as an analogue to the Rosenzweig-Porter model for Floquet systems, capturing their localization phenomenology.

Findings

Shares key statistical properties with the original ensemble for eigenvalues and eigenstates

Defined as the outcome of a Dyson Brownian motion process

Numerical evidence supports the ensemble's relevance to Floquet many-body localization

Abstract

The Rosenzweig-Porter random matrix ensemble serves as a qualitative phenomenological model for the level statistics and fractality of eigenstates across the many-body localization transition in static systems. We propose a unitary (circular) analogue of this ensemble, which similarly captures the phenomenology of many-body localization in periodically driven (Floquet) systems. We define this ensemble as the outcome of a Dyson Brownian motion process. We show numerical evidence that this ensemble shares some key statistical properties with the Rosenzweig-Porter ensemble for both the eigenvalues and the eigenstates.