Related papers: Anderson localization on random regular graphs
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 point of the Anderson transition and the delocalized phase.…
We combine numerical diagonalization with a semi-analytical calculations to prove the existence of the intermediate non-ergodic but delocalized phase in the Anderson model on disordered hierarchical lattices. We suggest a new generalized…
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 precision and abundance of our exact diagonalization data (both…
We study the Anderson transition on a generic model of random graphs with a tunable branching parameter $1<K\le 2$, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a…
We implement an efficient strong-disorder renormalization-group (SDRG) procedure to study disordered tight-binding models in any dimension and on the Erdos-Renyi random graphs, which represent an appropriate infinite dimensional limit. Our…
The Anderson transition on random graphs draws interest through its resemblance to the many-body localization (MBL) transition with similarly debated properties. In this Letter, we construct a unitary Anderson model on Small-World graphs to…
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. Properties of eigenstate and energy level correlations in…
We present a renormalization group analysis of the problem of Anderson localization on a Random Regular Graph (RRG) which generalizes the renormalization group of Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional…
Anderson localization on random regular graphs (RRG) serves as a toy-model of many-body localization (MBL). We explore the transition for ergodicity to localization on RRG with large connectivity $m$. In the analytical part, we focus on the…
We study Anderson localisation on high-dimensional graphs with spatial structure induced by long-ranged but distance-dependent hopping. To this end, we introduce a class of models that interpolate between the short-range Anderson model on a…
We discuss the dependence of the critical properties of the Anderson model on the dimension $d$ in the language of $\beta$-function and renormalization group recently introduced in Ref.[arXiv:2306.14965] in the context of Anderson…
We describe a large disorder renormalization group (LDRG) method for the Anderson model of localization in one dimension which decimates eigenstates based on the size of their wavefunctions rather than their energy. We show that our LDRG…
We present strong numerical evidence for the existence of a localization-delocalization transition in the eigenstates of the 1-D Anderson model with long-range hierarchical hopping. Hierarchical models are important because of the…
We present a full description of the nonergodic properties of wavefunctions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are characterized by two critical localization…
We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results indicate that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the…
Building on recent progress in the study of Anderson and many-body localization via the renormalization group (RG), we examine the scaling theory of localization in the quantum Random Energy Model (QREM). The QREM is known to undergo a…
We propose a new viewpoint on the study of localization transitions in disordered quantum systems, showing how critical properties can be seen also as a geometric transition in the data space generated by the classically encoded…
We determine the phase diagram of the Anderson tight-binding model on random regular graphs with Gaussian disorder and sufficiently large degree. In particular, we prove that if the degree is fixed and the number of vertices goes to…
The Anderson delocalization-localization transition is studied in multilayered systems with randomly placed interlayer bonds of density $p$ and strength $t$. In the absence of diagonal disorder (W=0), following an appropriate perturbation…
This work is a generic advance in the study of delocalized (ergodic) to localized (non-ergodic) wave propagation phenomena in the presence of disorder. There is an urgent need to better understand the physics of extreme value process in the…