Contributor info: Dr Wouter Buijsman

Wouter Buijsman, Yevgeny Bar Lev

SciPost Phys. 12, 082 (2022) · published 3 March 2022 | Toggle abstract · pdf

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.

Wouter Buijsman, Vladimir Gritsev, Vadim Cheianov

SciPost Phys. 4, 038 (2018) · published 25 June 2018 | Toggle abstract · pdf

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.