Statistical mechanics provides a framework for describing the physics of large, complex
many-body systems using only a few macroscopic parameters to determine the state of the …

We study Anderson localization in disordered tight-binding models on hyperbolic lattices.
Such lattices are geometries intermediate between ordinary two-dimensional crystalline …

We present a renormalization group (RG) analysis of the problem of Anderson localization
on a random regular graph (RRG) which generalizes the RG of Abrahams, Anderson …

This article reviews recent progress in understanding the physics of many-body localisation
(MBL) in disordered and interacting quantum many-body systems, from the perspective of …

Despite enormous efforts devoted to the study of the many-body localization (MBL)
phenomenon, the nature of the high-energy behavior of the Heisenberg spin chain in a …

We perform a thorough and complete analysis of the Anderson localization transition on
several models of random graphs with regular and random connectivity. The unprecedented …

It is believed that the two-dimensional (2D) Anderson model exhibits localization for any
nonzero disorder in the thermodynamic limit and it is also well known that the finite-size …

In the field of ergodicity-breaking phases, it has been recognized that quantum avalanches
can destabilize many-body localization at a wide range of disorder strengths. This has 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 …

We study the spectral properties of the adjacency matrix in the giant connected component
of Erdös-Rényi random graphs, with average degree p and randomly distributed hopping …