SciPost Phys. 11, 101 (2021) ·
published 6 December 2021
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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.
SciPost Phys. 8, 049 (2020) ·
published 1 April 2020
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We study the wave function localization properties in a d-dimensional model
of randomly spaced particles with isotropic hopping potential depending solely
on Euclidean interparticle distances. Due to the generality of this model
usually called the Euclidean random matrix model, it arises naturally in
various physical contexts such as studies of vibrational modes, artificial
atomic systems, liquids and glasses, ultracold gases and photon localization
phenomena. We generalize the known Burin-Levitov renormalization group
approach, formulate universal conditions sufficient for localization in such
models and inspect a striking equivalence of the wave function spatial decay
between Euclidean random matrices and translation-invariant long-range lattice
models with a diagonal disorder.
