SciPost Phys. 12, 082 (2022) ·
published 3 March 2022
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.
SciPost Phys. 4, 038 (2018) ·
published 25 June 2018
We study the eigenstates of a paradigmatic model of many-body localization in
the Fock basis constructed out of the natural orbitals. By numerically studying
the participation ratio, we identify a sharp crossover between different phases
at a disorder strength close to the disorder strength at which subdiffusive
behaviour sets in, significantly below the many-body localization transition.
We repeat the analysis in the conventionally used computational basis, and show
that many-body localized eigenstates are much stronger localized in the Fock
basis constructed out of the natural orbitals than in the computational basis.
Dr Buijsman: "We thank the referee for revie..."
in Submissions | report on Circular Rosenzweig-Porter random matrix ensemble