Emergent fractal phase in energy stratified random models

TL;DR

This paper investigates how partial correlations in long-range disordered models influence localization, revealing an emergent fractal phase and non-ergodic delocalization through analytical and numerical methods.

Contribution

It introduces an energy-stratified spectral structure for correlated hopping terms and generalizes Dyson Brownian motion and cavity approaches to analyze these models.

Findings

Partial correlations induce non-ergodic delocalization.

Emergent fractal phase observed in correlated models.

Analytical and numerical evidence supports new localization phenomena.

Abstract

We study the effects of partial correlations in kinetic hopping terms of long-range disordered random matrix models on their localization properties. We consider a set of models interpolating between fully-localized Richardson's model and the celebrated Rosenzweig-Porter model (with implemented translation-invariant symmetry). In order to do this, we propose the energy-stratified spectral structure of the hopping term allowing one to decrease the range of correlations gradually. We show both analytically and numerically that any deviation from the completely correlated case leads to the emergent non-ergodic delocalization in the system unlike the predictions of localization of cooperative shielding. In order to describe the models with correlated kinetic terms, we develop the generalization of the Dyson Brownian motion and cavity approaches basing on stochastic matrix process with independent rank-one matrix increments and examine its applicability to the above set of models.