Anderson localization on the Bethe lattice: non-ergodicity of extended states

Abstract

Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal dimensions $f(\alpha )$ defined in Eq.(3), remains positive for $\alpha$ noticeably far from 1 even when the disorder is several times weaker than the one which leads to the Anderson localization, i.e. the ergodicity can be reached only in the absence of disorder. The one-particle multifractality on the Bethe lattice signals on a possible inapplicability of the equipartition law to a generic many-body quantum system as long as it remains isolated.

5 pages, 3 figures + 4 pages supplemental material. arXiv admin note: text overlap with arXiv:1401.0019

References in corpus (3)

• Anderson Transitions
• Ergodicity breaking in a model showing many-body localization
• Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder

Cited by in corpus (207)

• Many-body localization edge in the random-field Heisenberg chain
• Many-body localization: an introduction and selected topics
• Universal dynamics and renormalization in many body localized systems
• Integrals of motion in the Many-Body localized phase
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• The Ergodic Side of the Many-Body Localization Transition
• Multifractal Scalings across the Many-Body Localization Transition
• Many-body localization characterized from a one-particle perspective
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
• One-dimensional quasicrystals with power-law hopping
• A random matrix model with localization and ergodic transitions
• Anomalous thermalization in ergodic systems
• Low-frequency conductivity in many-body localized systems
• Dynamics at the Many-Body Localization Transition
• Anderson localization on random regular graphs
• Early breakdown of area-law entanglement at many-body delocalization transition
• Many-body mobility edge in a mean-field quantum spin glass
• Non-ergodic phases in strongly disordered random regular graphs
• Correlation-induced localization
• Scaling theory of the Anderson transition in random graphs: ergodicity and universality
• Many-Body Localization in the Age of Classical Computing
• Kosterlitz-Thouless scaling at many-body localization phase transitions
• Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
• Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
• Rare thermal bubbles at the many-body localization transition from the Fock space point of view
• From Anderson localization on Random Regular Graphs to Many-Body localization
• Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
• Statistics of eigenstates near the localization transition on random regular graphs
• From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
• Extended nonergodic states in disordered many-body quantum systems
• Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge
• Return probability for the Anderson model on the random regular graph
• Many-body localization transition with power-law interactions: Statistics of eigenstates
• Delocalized Glassy Dynamics and Many Body Localization
• Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems
• The forward approximation as a mean field approximation for the Anderson and Many Body Localization transitions
• Critical behavior at the localization transition on random regular graphs
• Duality in power-law localization in disordered one-dimensional systems
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Probing many-body quantum chaos with quantum simulators
• Two critical localization lengths in the Anderson transition on random graphs
• Critical properties of the Anderson localization transition and the high dimensional limit
• Sub-diffusion in the Anderson model on random regular graph
• Multifractality of wave functions on a Cayley tree: From root to leaves
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• Total correlations of the diagonal ensemble herald the many-body localization transition
• The Lévy-Rosenzweig-Porter random matrix ensemble
• Anderson transition on the Bethe lattice: an approach with real energies
• Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain
• Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
• Non-Ergodic Delocalization in the Rosenzweig-Porter Model
• Multifractality meets entanglement: relation for non-ergodic extended states
• Many-body localization in incommensurate models with a mobility edge
• Multifractality and its role in anomalous transport in the disordered XXZ spin-chain
• A mean-field theory of nearly many-body localized metals
• Multifractality without fine-tuning in a Floquet quasiperiodic chain
• Eigenstate correlations around many-body localization transition
• Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach
• Localized systems coupled to small baths: from A${}_{nderson}$ to Z${}_{eno}$
• Counting local integrals of motion in disordered spinless-fermion and Hubbard chains
• Level statistics and localization transitions of Lévy matrices
• Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization
• Avalanche induced co-existing localised and thermal regions in disordered chains
• Thermal inclusions: how one spin can destroy a many-body localized phase
• Local Kesten--McKay law for random regular graphs
• Localization transition on the Random Regular Graph as an unstable tricritical point in a log-normal Rosenzweig-Porter random matrix ensemble
• Clustering of non-ergodic eigenstates in quantum spin glasses
• Quantum Levy flights and multifractality of dipolar excitations in a random system
• From ergodic to non-ergodic chaos in Rosenzweig-Porter model
• Non-ergodic extended states in the SYK model
• Multifractal metal in a disordered Josephson Junction Array
• Weak integrability breaking: chaos with integrability signature in coherent diffusion
• Spin subdiffusion in disordered Hubbard chain
• Many-body localization caused by temporal disorder
• Observation of many-body Fock space dynamics in two dimensions
• Chaos and quantum scars in Bose-Josephson junction coupled to a bosonic mode
• Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase
• Universality in Anderson localization on random graphs with varying connectivity
• Anomalous dynamics in the ergodic side of the Many-Body Localization transition and the glassy phase of Directed Polymers in Random Media
• Sub-diffusive Thouless time scaling in the Anderson model on random regular graphs
• A minimal model of many body localization
• Universal dynamics of density correlations at the transition to many-body localized state
• Localisation on certain graphs with strongly correlated disorder
• Energy diffusion in the ergodic phase of a many body localizable spin chain
• Non-ergodic extended phase of the Quantum Random Energy model
• Large deviation function for the number of eigenvalues of sparse random graphs inside an interval
• Many-Body-Localization Transition : strong multifractality spectrum for matrix elements of local operators
• Local entanglement structure across a many-body localization transition
• Many-Body Quantum Chaos and Space-time Translational Invariance
• Distinctive response of many-body localized systems to strong electric field
• Critical behavior of the Anderson model on the Bethe lattice via a large-deviation approach
• Coexistence of localization and transport in many-body two-dimensional Aubry-André models
• Dynamics of quasiperiodically driven spin systems
• The general approach to the critical phase with coupled quasiperiodic chains
• Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
• Quantum ergodicity in the many-body localization problem
• Single-Particle Mobility Edge without Disorder
• Renormalization Group Analysis of the Anderson Model on Random Regular Graphs
• Self-averaging in many-body quantum systems out of equilibrium. II. Approach to the localized phase
• The effect of anisotropy of long-range hopping on localization in three-dimensional lattices
• Revisiting classical and quantum disordered systems from the unifying perspective of large deviations
• Spread of wave packets in disordered hierarchical lattices
• Scaling up the Anderson transition in random-regular graphs
• Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States
• Many Body Localization Transition in the strong disorder limit : entanglement entropy from the statistics of rare extensive resonances
• Localization and criticality in antiblockaded 2D Rydberg atom arrays
• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
• Localization and chaos in a spin glass model with random fields: Mapping to the localization problem in a Bethe lattice with a correlated disorder
• Entanglement critical length at the many-body localization transition
• Multifractality in non-unitary random dynamics
• Role of Fock-space correlations in many-body localization
• Glassy properties of Anderson localization: pinning, avalanches and chaos
• Anisotropy-mediated reentrant localization
• Sensitivity of (multi)fractal eigenstates to a perturbation of the Hamiltonian
• Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations
• Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model
• Delocalized charge carriers in strongly disordered t-J model
• Renormalization to localization without a small parameter
• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• Ergodicity-to-localization transition on random regular graphs with large connectivity and in many-body quantum dots
• Anomalous diffusion and localization in a positionally disordered quantum spin array
• Transient and persistent particle subdiffusion in a disordered chain coupled to bosons
• Fully localized and partially delocalized states in the tails of Erdös-Rényi graphs in the critical regime
• Interacting Thermofield Doubles and Critical Behavior in Random Regular Graphs
• Finite temperature disordered bosons in two dimensions
• Many-body localization transition in a frustrated XY chain
• Multifractality of random eigenfunctions and generalization of Jarzynski equality
• Thermalization and many-body localization in systems under dynamic nuclear polarization
• Genuine localisation transition in a long-range hopping model
• Transport in the non-ergodic extended phase of interacting quasiperiodic systems
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• Diffusive to non-ergodic dipolar transport in a dissipative atomic medium
• Eigenstate localization in a many-body quantum system
• From Ergodicity to Many-Body Localization in a One-Dimensional Interacting Non-Hermitian Stark System
• Localization transition in random Levy matrices : multifractality of eigenvectors in the localized phase and at criticality
• Anatomy of the eigenstates distribution: a quest for a genuine multifractality
• Robust non-ergodicity of ground state in the $\beta$ ensemble
• Anderson transition and mobility edges on hyperbolic lattices with randomly connected boundaries
• Mobility Edge in the Anderson model on partially disordered random regular graphs
• Anatomy of the fragmented Hilbert space: eigenvalue tunneling, quantum scars and localization in the perturbed random regular graph
• Dynamical Signatures of Chaos to Integrability Crossover in $2\times 2$ Generalized Random Matrix Ensembles
• Localization spectrum of a bath-coupled generalized Aubry-André model in the presence of interactions
• Ergodic-localized junctions in periodically-driven systems
• Quantum ergodicity for the Anderson model on regular graphs
• Resonances and Partial Delocalization on the Complete Graph
• From entropic to energetic barriers in glassy dynamics: The Barrat-Mézard trap model on sparse networks
• Large scale behavior of the energy spectra of the quantum random antiferromagnetic Ising chain with mixed transverse and longitudinal fields
• Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization
• Dynamics and Asymptotics of Correlations in a Many-Body Localized System
• Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
• Classical route to ergodicity and scarring in collective quantum systems
• Random Transverse Field Spin-Glass Model on the Cayley tree : phase transition between the two Many-Body-Localized Phases
• Transport in deformed centrosymmetric networks
• Fractal Universality in Near-Threshold Magnetic Lanthanide Dimers
• An analysis of localization transitions using non-parametric unsupervised learning
• Localization in random bipartite graphs: numerical and empirical study
• Self-duality of One-dimensional Quasicrystals with Spin-Orbit Interaction
• Average diagonal entropy in non-equilibrium isolated quantum systems
• Multifractality and statistical localization in highly heterogeneous random networks
• Renormalization group for Anderson localization on high-dimensional lattices
• Localization crossover and subdiffusive transport in a classical facilitated network model of a disordered, interacting quantum spin chain
• Many-body localization of 1D disordered impenetrable two-component fermions
• Electron-phonon cooling power in Anderson insulators
• Coherent forward scattering as a robust probe of multifractality in critical disordered media
• Particle dynamics and ergodicity-breaking in twisted-bilayer optical lattices
• Critical dynamics of long-range quantum disordered systems
• Localization transition in non-Hermitian systems depending on reciprocity and hopping asymmetry
• Spectral properties, localization transition and multifractal eigenvectors of the Laplacian on heterogeneous networks
• Inner non-Hermitian skin effect on Bethe lattice
• Imbalance for a family of one-dimensional incommensurate models with mobility edges
• Single-particle localization in a two-dimensional Rydberg spin system
• How periodic driving stabilises and destabilises Anderson localisation on random trees
• Renormalization-Group Analysis of the Many-Body Localization Transition in the Random-Field XXZ Chain
• Robust extended states in Anderson model on partially disordered random regular graphs
• Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach
• Characterizing The Many-Body Localization via Studying State Sensitivity to Boundary Conditions
• Quantum logarithmic multifractality
• Selective final state spectroscopy and multifractality in two-component ultracold Bose-Einstein condensates: a numerical study
• Many-body localization of ${\mathbb{Z}}_3$ Fock parafermions
• Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space
• Finite size scaling for the Many-Body-Localization Transition : finite-size-pseudo-critical points of individual eigenstates
• Scaling analysis and renormalization group on the mobility edge in the quantum random energy model
• Localization of eigenvectors of non-Hermitian banded noisy Toeplitz matrices
• Intermittency as metastability: a predictive approach to evolution in disordered environments
• $L^p$ norms and support of eigenfunctions on graphs
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Classes of non-Gaussian random matrices: long-range eigenvalue correlations and non-ergodic extended eigenvectors
• Fluctuation driven transitions in localized insulators: Intermittent metallicity and path chaos precede delocalization
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes
• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree
• Random cubic graph embedded in a hypercube: Entanglement spectrum and many-body localization
• Entanglement Entropy on the Cayley Tree
• Circular Rosenzweig-Porter random matrix ensemble
• Localization and fractality in disordered Russian Doll model
• Unsupervised Techniques to Detect Quantum Chaos
• 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
• Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder
• Evolution of grammatical forms: some quantitative approaches
• Localization properties of the sparse Barrat-Mézard trap model
• Effect of spin-orbit coupling in one-dimensional quasicrystals with power-law hopping
• Distinct Critical Behaviors from the Same State in Quantum Spin and Population Dynamics Perspectives
• Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices
• Information Bounds on phase transitions in disordered systems
• Disordered statistical physics in low dimensions: extremes, glass transition, and localization
• Critical Dynamics of the Anderson Transition on Small-World Graphs