We re-examine attempts to study the many-body localization transition using measures that
are physically natural on the ergodic/quantum chaotic regime of the phase diagram. Using …

The article reviews the physics of Anderson localization on random regular graphs (RRG)
and its connections to many-body localization (MBL) in disordered interacting systems …

In this paper we study the many-body localization (MBL) transition and relate it to the
eigenstate structure in the Fock space. Besides the standard entanglement and multifractal …

The Anderson transition in random graphs has raised great interest, partly out of the hope
that its analogy with the many-body localization (MBL) transition might lead to a better …

Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in
the Anderson model on random regular graphs (RRG) are studied. We consider the critical …

We consider the static and the dynamic phases in a Rosenzweig-Porter (RP) random matrix
ensemble with a distribution of off-diagonal matrix elements of the form of the large-deviation …

Multifractal dimensions allow for characterizing the localization properties of states in
complex quantum systems. For ergodic states the finite-size versions of fractal dimensions …

In this paper we propose a new perspective to analyze the many-body localization (MBL)
transition when recast in terms of a single-particle tight-binding model in the space of many …

We study the return probability for the Anderson model on the random regular graph and
give evidence of the existence of two distinct phases: a fully ergodic and nonergodic one. In …

A central theoretical issue at the core of the current research on many-body localization
(MBL) consists in characterizing the statistics of rare long-range resonances in many-body …