Two critical localization lengths in the Anderson transition on random graphs

Abstract

We present a full description of the nonergodic properties of wavefunctions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are characterized by two critical localization lengths: the largest one describes localization along rare branches and diverges with a critical exponent ${\nu }_{\parallel }=1$ at the transition. The second length, which describes localization along typical branches, reaches at the transition a finite universal value (which depends only on the connectivity of the graph), with a singularity controlled by a new critical exponent ${\nu }_{\perp }=1/2$. We show numerically that these two localization lengths control the finite-size scaling properties of key observables: wavefunction moments, correlation functions and spectral statistics. Our results are identical to the theoretical predictions for the typical localization length in the many-body localization transition, with the same critical exponent. This strongly suggests that the two transitions are in the same universality class and that our techniques could be directly applied in this context.

arXiv comment6 pages, 3 figures; Corresponds to the published version

References in corpus (65)

• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Localization of interacting fermions at high temperature
• Many-body localization, thermalization, and entanglement
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
• Many-body localization: an introduction and selected topics
• Recent progress in many-body localization
• Corrections to scaling at the Anderson transition
• The Ergodic Side of the Many-Body Localization Transition
• Anderson localization on the Bethe lattice: non-ergodicity of extended states
• Multifractal Scalings across the Many-Body Localization Transition
• Ergodicity breaking in a model showing many-body localization
• A random matrix model with localization and ergodic transitions
• Many-body delocalization as a quantum avalanche
• Multifractal finite-size-scaling and universality at the Anderson transition
• Anderson localization on random regular graphs
• Non-ergodic phases in strongly disordered random regular graphs
• Scaling theory of the Anderson transition in random graphs: ergodicity and universality
• 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
• Universal behavior beyond multifractality in quantum many-body systems
• Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
• Statistics of eigenstates near the localization transition on random regular graphs
• Non-ergodic metallic and insulating phases of Josephson junction chains
• From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
• Extended nonergodic states in disordered many-body quantum systems
• Return probability for the Anderson model on the random regular graph
• Superconductor-Insulator transition and energy localization
• Delocalized Glassy Dynamics and Many Body Localization
• Critical behavior at the localization transition on random regular graphs
• Critical properties of the Anderson localization transition and the high dimensional limit
• Multifractality of wave functions on a Cayley tree: From root to leaves
• Survival probability in Generalized Rosenzweig-Porter random matrix ensemble
• Anderson transition on the Bethe lattice: an approach with real energies
• Many-body Multifractality throughout Bosonic Superfluid and Mott Insulator Phases
• Localization transition on complex networks via spectral statistics
• Multifractal metal in a disordered Josephson Junction Array
• Extended States in a Lifshitz Tail Regime for Random Schrödinger Operators on Trees
• From ergodic to non-ergodic chaos in Rosenzweig-Porter model
• Weak Disorder Expansion for the Anderson Model on a Tree
• Percolation in Fock space as a proxy for many-body localisation
• Finite size correction to the spectrum of regular random graphs: an analytical solution
• Anderson localization on the Cayley tree : multifractal statistics of the transmission at criticality and off criticality
• Quantum computing of delocalization in small-world networks
• Anderson transition on the Cayley tree as a traveling wave critical point for various probability distributions
• Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase
• Localization-Delocalization Transition of Electron States in a Disordered Quantum Small World Network
• Localization in random fractal lattices
• Delocalization and ergodicity of the Anderson model on Bethe lattices
• 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
• Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
• Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder
• Statistics of renormalized on-site energies and renormalized hoppings for Anderson localization models in dimensions d=2 and d=3
• Finite-size scaling with respect to interaction and disorder strength at the many-body localization transition
• Finite-size scaling of the Shannon-Rényi entropy in two-dimensional systems with spontaneously broken continuous symmetry
• Large Deviations of Correlation Functions in Random Magnets
• Localization transition in random Levy matrices : multifractality of eigenvectors in the localized phase and at criticality
• Many-body localization in the Fock space of natural orbitals
• An improved Belief Propagation algorithm finds many Bethe states in the random field Ising model on random graphs
• Quantum Monte Carlo detection of SU(2) symmetry breaking in the participation entropies of line subsystems

Cited by in corpus (56)

• Distinguishing localization from chaos: challenges in finite-size systems
• Many-Body Localization in the Age of Classical Computing
• 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
• The Many-Body localization transition in the Hilbert space
• Non-Hermitian Many-Body Localization with Open Boundaries
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Sub-diffusion in the Anderson model on random regular graph
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain
• Eigenstate correlations around many-body localization transition
• Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization
• Localization transition on the Random Regular Graph as an unstable tricritical point in a log-normal Rosenzweig-Porter random matrix ensemble
• From ergodic to non-ergodic chaos in Rosenzweig-Porter model
• Fock-space anatomy of eigenstates across the many-body localisation transition
• 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
• Localisation on certain graphs with strongly correlated disorder
• Hilbert-space fragmentation, multifractality, and many-body localization
• Many-body localization in large systems: Matrix-product-state approach
• Renormalization Group Analysis of the Anderson Model on Random Regular Graphs
• Scaling up the Anderson transition in random-regular graphs
• Role of Fock-space correlations in many-body localization
• Renormalization to localization without a small parameter
• Ergodicity-to-localization transition on random regular graphs with large connectivity and in many-body quantum dots
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• The Fock-space landscape of many-body localisation
• Anatomy of the eigenstates distribution: a quest for a genuine multifractality
• Anatomy of the fragmented Hilbert space: eigenvalue tunneling, quantum scars and localization in the perturbed random regular graph
• Many-body localization with synthetic gauge fields in disordered Hubbard chains
• Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization
• Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
• Statistics of systemwide correlations in the random-field XXZ chain: Importance of rare events in the many-body localized phase
• Finite-size prethermalization at the chaos-to-integrable crossover
• Multifractality and statistical localization in highly heterogeneous random networks
• Renormalization group for Anderson localization on high-dimensional lattices
• Coherent forward scattering as a robust probe of multifractality in critical disordered media
• Localization crossover and subdiffusive transport in a classical facilitated network model of a disordered, interacting quantum spin chain
• Critical dynamics of long-range quantum disordered systems
• Spectral properties, localization transition and multifractal eigenvectors of the Laplacian on heterogeneous networks
• Robust extended states in Anderson model on partially disordered random regular graphs
• How periodic driving stabilises and destabilises Anderson localisation on random trees
• Soft modes in vector spin glass models on sparse random graphs
• Quantum logarithmic multifractality
• Solving Free Fermion Problems on a Quantum Computer
• Scaling theory of fading ergodicity
• Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space
• Quantum magnetism on small-world networks
• Spectral Multifractality and Emergent Energyscales Across the Many-Body Localisation Transition
• Multifractality in high-dimensional graphs induced by correlated radial disorder
• Anderson localisation in spatially structured random graphs
• The Wishart--Rosenzweig--Porter random matrix ensemble
• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree
• Critical Dynamics of the Anderson Transition on Small-World Graphs