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.
Cited by 2
De Tomasi et al., Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase
Phys. Rev. B 106, 094204 (2022) [Crossref]
Tarzia, Fully localized and partially delocalized states in the tails of Erdös-Rényi graphs in the critical regime
Phys. Rev. B 105, 174201 (2022) [Crossref]