Circular Rosenzweig-Porter random matrix ensemble
Wouter Buijsman
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.
Topics & Concepts
Random matrixEigenvalues and eigenvectorsCircular ensembleUnitary stateStatistical physicsBrownian motionFloquet theoryStatistical ensemblePhenomenology (philosophy)MathematicsEnsemble forecastingMatrix (chemical analysis)PhysicsCanonical ensembleQuantum mechanicsComputer scienceArtificial intelligenceStatisticsMonte Carlo methodPhilosophyEpistemologyComposite materialPolitical scienceNonlinear systemMaterials scienceLawQuantum many-body systemsOpinion Dynamics and Social InfluenceStatistical Mechanics and Entropy