Circular Rosenzweig-Porter random matrix ensemble

2021/11/15 by Buijsman, Wouter, Lev, Yevgeny Bar · 2 citations
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2111.08031

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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• Entanglement in bipartite systems with symmetry: coupled chaotic kicked Bose-Hubbard systems
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the β-ensemble

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