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Circular Rosenzweig-Porter random matrix ensemble

Wouter Buijsman, Yevgeny Bar Lev

SciPost Phys. 12, 082 (2022) · published 3 March 2022

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.

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