From Anderson localization on Random Regular Graphs to Many-Body localization

Abstract

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 delocalized and localized phases, as well at criticality, are discussed. In the many-body part, models with short-range and power-law interactions are considered, as well as the quantum-dot model representing the limit of the "most long-range" interaction. Central themes -- which are common to the RRG and MBL problems -- include ergodicity of the delocalized phase, localized character of the critical point, strong finite-size effects, and fractal scaling of eigenstate correlations in the localized phase.

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• Many-body localization in large systems: Matrix-product-state approach
• Critical behavior of the Anderson model on the Bethe lattice via a large-deviation approach
• Renormalization Group Analysis of the Anderson Model on Random Regular Graphs
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• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
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• The Fock-space landscape of many-body localisation
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• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree
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• Circular Rosenzweig-Porter random matrix ensemble
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• Anderson localisation in spatially structured random graphs
• Observation of Localization Using a Noisy Quantum Computer
• Unsupervised Techniques to Detect Quantum Chaos
• Information Bounds on phase transitions in disordered systems
• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain
• Anderson Localization on Husimi Trees and its implications for Many-Body localization
• Localization properties of the sparse Barrat-Mézard trap model
• Path Counting on Tree-like Graphs with a Single Entropic Trap: Critical Behavior and Finite Size Effects
• Critical Dynamics of the Anderson Transition on Small-World Graphs
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