Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder

Abstract

Our recently established criterion for the formation of extended states on tree graphs in the presence of disorder is shown to have the surprising implication that for bounded random potentials, as in the Anderson model, there is no transition to a spectral regime of Anderson localization, in the form usually envisioned, unless the disorder is strong enough.

References in corpus (3)

• The many-body localization phase transition
• Extended States in a Lifshitz Tail Regime for Random Schrödinger Operators on Trees
• Lifshitz tails on the Bethe lattice: a combinatorial approach

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• Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
• The Many-Body localization transition in the Hilbert space
• Two critical localization lengths in the Anderson transition on random graphs
• Many-Body Localization: Stability and Instability
• Multifractality of wave functions on a Cayley tree: From root to leaves
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization
• Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase
• Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs
• Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
• Quantum Walks on Trees with Disorder: Decay, Diffusion, and Localization
• Many-Body Localization in a finite-range Sachdev-Ye-Kitaev model
• The Large Connectivity Limit of the Anderson Model on Tree Graphs
• Spectral Transition for Random Quantum Walks on Trees
• Genuine localisation transition in a long-range hopping model
• Localization spectrum of a bath-coupled generalized Aubry-André model in the presence of interactions
• Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
• Semi-discrete semi-linear parabolic SPDEs
• Zero Measure and Singular Continuous Spectra for Quantum Graphs
• Progress in the mathematical theory of quantum disordered systems
• Boosted Simon-Wolff Spectral Criterion and Resonant Delocalization
• Identifying mobility edge from finite temperature spectral form factor