Emergent fractal phase in energy stratified random models

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.

27 pages, 6 figures

References in corpus (9)

• Anderson Transitions
• Many-body localization edge in the random-field Heisenberg chain
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• The Lévy-Rosenzweig-Porter random matrix ensemble
• Robustness of delocalization to the inclusion of soft constraints in long-range random models
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• Mobility edge and multifractality in a periodically driven Aubry-André model
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• Intermittency of dynamical phases in a quantum spin glass

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• Fully localized and partially delocalized states in the tails of Erdös-Rényi graphs in the critical regime
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• Anatomy of the eigenstates distribution: a quest for a genuine multifractality
• Robust non-ergodicity of ground state in the $\beta$ ensemble
• Long-range spectral statistics of the Rosenzweig-Porter model
• Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems
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• Robust extended states in Anderson model on partially disordered random regular graphs
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping
• Refined cyclic renormalization group in Russian Doll model
• Efficient circular Dyson Brownian motion algorithm
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• Circular Rosenzweig-Porter random matrix ensemble
• Replica approach to the generalized Rosenzweig-Porter model
• Localization and fractality in disordered Russian Doll model
• Robust Correlation-Induced Localization Under Time-Reversal Symmetry Breaking
• Anderson Localization on Husimi Trees and its implications for Many-Body localization
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder