Circular Rosenzweig-Porter random matrix ensemble

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. In this talk, I will propose a unitary (circular) analogue of the Rosenzweig-Porter ensemble, which similarly captures the phenomenology of many-body localization in periodically driven (Floquet) systems. The ensemble is defined as the outcome of a Dyson Brownian motion process. I will show numerical evidence that the circular analogue shares some key properties with the Rosenzweig-Porter ensemble for both the eigenvalues and the eigenstates.