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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.