Return probability for the Anderson model on the random regular graph

Abstract

We study the return probability for the Anderson model on the random regular graph and give evidence of the existence of two distinct phases: a fully ergodic and nonergodic one. In the ergodic phase, the return probability decays polynomially with time with oscillations, being the attribute of the Wigner-Dyson-like behavior, while in the nonergodic phase the decay follows a stretched exponential decay.We give a phenomenological interpretation of the stretched exponential decay in terms of a classical random walker. Furthermore, comparing typical and mean values of the return probability, we show how to differentiate an ergodic phase from a nonergodic one. We benchmark this method first in two random matrix models, the power-law random banded matrices, and the Rosenzweig-Porter matrices, which host both phases. Second, we apply this method to the Anderson model on the random regular graph to give further evidence of the existence of the two phases.

arXiv comment10 pages, 4 figures, 88 references (main text) + 5 pages, 9 figures (appendices)

References in corpus (60)

• 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
• The many-body localization phase transition
• The Kernel Polynomial Method
• Many-body localization edge in the random-field Heisenberg chain
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
• Integrals of motion in the Many-Body localized phase
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
• Theory of the many-body localization transition in one dimensional systems
• Recent progress in many-body localization
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Extended slow dynamical regime close to the many-body localization transition
• The Ergodic Side of the Many-Body Localization Transition
• Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system
• Anderson localization on the Bethe lattice: non-ergodicity of extended states
• A criterion for many-body localization-delocalization phase transition
• Ergodicity breaking in a model showing many-body localization
• Multifractality and critical fluctuations at the Anderson transition
• Many-body localization characterized from a one-particle perspective
• Review: Local Integrals of Motion in Many-Body Localized systems
• A random matrix model with localization and ergodic transitions
• Anomalous thermalization in ergodic systems
• Anderson localization on random regular graphs
• Griffiths effects and slow dynamics in nearly many-body localized systems
• Non-ergodic phases in strongly disordered random regular graphs
• Scaling theory of the Anderson transition in random graphs: ergodicity and universality
• Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
• Density propagator for many-body localization: finite size effects, transient subdiffusion, and exponential decay
• Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
• Quantum Mutual Information as a Probe for Many-Body Localization
• Transport in quasiperiodic interacting systems: from superdiffusion to subdiffusion
• Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance and out-of-time-ordered correlator
• Many-body localization phase transition: A simplified strong-randomness approximate renormalization group
• Delocalized Glassy Dynamics and Many Body Localization
• Signatures of the many-body localization transition in the dynamics of entanglement and bipartite fluctuations
• Duality in power-law localization in disordered one-dimensional systems
• Spin transport of weakly disordered Heisenberg chain at infinite temperature
• Critical properties of the Anderson localization transition and the high dimensional limit
• Typicality approach to the optical conductivity in thermal and many-body localized phases
• Multifractality of wave functions on a Cayley tree: From root to leaves
• Many-body localization beyond eigenstates in all dimensions
• Shielding and localization in presence of long range hopping
• Finite size scaling bounds on many-body localized phase transitions
• Dynamical scaling for critical states: is Chalker's ansatz valid for strong fractality?
• Power-law decay exponents: a dynamical criterion for predicting thermalization
• Finite temperature transport in disordered Heisenberg chains
• Power-law random banded matrices and ultrametric matrices: eigenvector distribution in the intermediate regime
• Emergent local integrals of motion without a complete set of localized eigenstates
• Integrals of motion for one-dimensional Anderson localized systems
• Multifractal states in self-consistent theory of localization: analytical solution
• The Link between Integrability, Level Crossings, and Exact Solution in Quantum Models
• Return probability and scaling exponents in the critical random matrix ensemble
• Levy flights and multifractality in quantum critical diffusion and in classical random walks on fractals
• Entanglement critical length at the many-body localization transition
• Generalized Dyson model: nature of zero mode and its implication in dynamics

Cited by in corpus (68)

• Multifractal Scalings across the Many-Body Localization Transition
• Distinguishing localization from chaos: challenges in finite-size systems
• Correlation-induced localization
• 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
• Statistics of eigenstates near the localization transition on random regular graphs
• Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Two critical localization lengths in the Anderson transition on random graphs
• Sub-diffusion in the Anderson model on random regular graph
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• Survival probability in Generalized Rosenzweig-Porter random matrix ensemble
• The Lévy-Rosenzweig-Porter random matrix ensemble
• Anderson transition on the Bethe lattice: an approach with real energies
• Multifractality meets entanglement: relation for non-ergodic extended states
• Multifractality and its role in anomalous transport in the disordered XXZ spin-chain
• Robustness of delocalization to the inclusion of soft constraints in long-range random models
• Phenomenology of the Prethermal Many-Body Localized Regime
• 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
• Non-ergodic delocalized phase with Poisson level statistics
• Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal 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
• Non-ergodic extended phase of the Quantum Random Energy model
• Self-averaging in many-body quantum systems out of equilibrium: Chaotic systems
• 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
• Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
• Self-averaging in many-body quantum systems out of equilibrium. II. Approach to the localized phase
• Scale-Invariant Survival Probability at Eigenstate Transitions
• Scaling up the Anderson transition in random-regular graphs
• Scale-invariant critical dynamics at eigenstate transitions
• Role of Fock-space correlations in many-body localization
• Anisotropy-mediated reentrant localization
• Random Cantor sets and mini-bands in local spectrum of quantum systems
• Renormalization to localization without a small parameter
• Ergodicity-to-localization transition on random regular graphs with large connectivity and in many-body quantum dots
• Interacting Thermofield Doubles and Critical Behavior in Random Regular Graphs
• 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
• Self-averaging in many-body quantum systems out of equilibrium: Time dependence of distributions
• Normal weak eigenstate thermalization
• Robust non-ergodicity of ground state in the $\beta$ ensemble
• 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
• Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization
• An analysis of localization transitions using non-parametric unsupervised learning
• Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
• The connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains
• Finite-size prethermalization at the chaos-to-integrable crossover
• 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
• Critical dynamics of long-range quantum disordered systems
• Robust extended states in Anderson model on partially disordered random regular graphs
• Effective delocalization in the one-dimensional Anderson model with stealthy disorder
• A Gaussian integral that counts regular graphs
• Quantum logarithmic multifractality
• Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder
• Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space
• Scaling analysis and renormalization group on the mobility edge in the quantum random energy model
• Critical quantum dynamics of observables at eigenstate transitions
• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree
• Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models
• Critical Dynamics of the Anderson Transition on Small-World Graphs
• Stabilizing confined quasiparticle dynamics in one-dimensional polar lattice gases