Delocalized Glassy Dynamics and Many Body Localization

Abstract

We analyze the unusual slow dynamics that emerges in the bad metal delocalized phase preceding the Many-Body Localization transition by using single-particle Anderson Localization on the Bethe lattice as a toy model of many-body dynamics in Fock space. We probe the dynamical evolution by measuring observables such as the imbalance and equilibrium correlation functions, which display slow dynamics and power-laws strikingly similar to the ones observed in recent simulations and experiments. We relate this unusual behavior to the non-ergodic spectral statistics found on Bethe lattices. We discuss different scenarii, such as a true intermediate phase which persists in the thermodynamic limit versus a glassy regime established on finite but very large time and length-scales only, and their implications for real space dynamical properties. In the latter, slow dynamics and power-laws extend on a very large time-window but are eventually cut-off on a time-scale that diverges at the MBL transition.

6 pages

References in corpus (29)

• Many body localization and thermalization in quantum statistical mechanics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
• Universal dynamics and renormalization in many body localized systems
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Theory of the many-body localization transition in one dimensional systems
• 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
• Universal properties of many-body delocalization transitions
• The Ergodic Side of the Many-Body Localization Transition
• Anderson localization on the Bethe lattice: non-ergodicity of extended states
• Ergodicity breaking in a model showing many-body localization
• Emergence of quantum chaos in finite interacting Fermi systems
• A random matrix model with localization and ergodic transitions
• Rare region effects and dynamics near the many-body localization transition
• Anomalous thermalization in ergodic systems
• Dynamics at the Many-Body Localization Transition
• 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
• Two-eigenfunction correlation in a multifractal metal and insulator
• Transport in quasiperiodic interacting systems: from superdiffusion to subdiffusion
• From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
• Slow Dynamics in a Two-Dimensional Anderson-Hubbard Model
• Level statistics and localization transitions of Lévy matrices
• Multifractal states in self-consistent theory of localization: analytical solution

Cited by in corpus (65)

• Many-body localization: an introduction and selected topics
• Distinguishing localization from chaos: challenges in finite-size systems
• Many-body localization and delocalization in large quantum chains
• Correlation-induced localization
• Rare thermal bubbles at the many-body localization transition from the Fock space point of view
• Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
• From Anderson localization on Random Regular Graphs to Many-Body localization
• Statistics of eigenstates near the localization transition on random regular graphs
• Time Evolution of Many-Body Localized Systems with the Flow Equation Approach
• Transport in quasiperiodic interacting systems: from superdiffusion to subdiffusion
• Return probability for the Anderson model on the random regular graph
• Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems
• The Many-Body localization transition in the Hilbert space
• 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
• Dynamics and Transport at the Threshold of Many-Body Localization
• Survival probability in Generalized Rosenzweig-Porter random matrix ensemble
• The Lévy-Rosenzweig-Porter random matrix ensemble
• 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
• From ergodic to non-ergodic chaos in Rosenzweig-Porter model
• Multifractal metal in a disordered Josephson Junction Array
• Non-ergodic delocalized phase with Poisson level statistics
• 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
• Dynamical Glass and Ergodization Times in Classical Josephson Junction Chains
• A minimal model of many body localization
• Sub-diffusive Thouless time scaling in the Anderson model on random regular graphs
• Localisation on certain graphs with strongly correlated disorder
• Non-ergodic extended phase of the Quantum Random Energy model
• Hilbert-space fragmentation, multifractality, and many-body localization
• Many-Body Quantum Chaos and Space-time Translational Invariance
• Critical behavior of the Anderson model on the Bethe lattice via a large-deviation approach
• Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
• Renormalization Group Analysis of the Anderson Model on Random Regular Graphs
• Quasi-Many-Body Localization of Interacting Fermions with Long-Range Couplings
• Scaling up the Anderson transition in random-regular graphs
• Role of Fock-space correlations in many-body localization
• Glassy properties of Anderson localization: pinning, avalanches and chaos
• 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
• A toy model for anomalous transport and Griffiths effects near the Many-Body Localization transition
• The Fock-space landscape of many-body localisation
• Eigenstate localization in a many-body quantum system
• 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
• 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
• Thermalization in the one-dimensional Salerno model lattice
• How periodic driving stabilises and destabilises Anderson localisation on random trees
• Robust extended states in Anderson model on partially disordered random 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
• Multifractality in high-dimensional graphs induced by correlated radial disorder
• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree
• Localization properties of the sparse Barrat-Mézard trap model
• Anderson Localization on Husimi Trees and its implications for Many-Body localization
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain
• Critical Dynamics of the Anderson Transition on Small-World Graphs