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 (9)

• Many body localization and thermalization in quantum statistical mechanics
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Ergodicity breaking in a model showing many-body localization
• Anomalous thermalization in ergodic systems
• Non-ergodic phases in strongly disordered random regular graphs
• Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
• From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
• Multifractal states in self-consistent theory of localization: analytical solution

Cited by in corpus (42)

• 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
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• 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
• 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
• 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
• Many-Body Quantum Chaos and Space-time Translational Invariance
• Critical behavior of the Anderson model on the Bethe lattice via a large-deviation approach
• Renormalization Group Analysis of the Anderson Model on Random Regular Graphs
• Scaling up the Anderson transition in random-regular graphs
• Quasi-Many-Body Localization of Interacting Fermions with Long-Range Couplings
• Role of Fock-space correlations in many-body localization
• 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
• Eigenstate localization in a many-body quantum system
• Mobility Edge in the Anderson model on partially disordered random regular graphs
• Robust non-ergodicity of ground state in the $\beta$ ensemble
• 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
• Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder
• Quantum logarithmic multifractality
• 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
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain
• Anderson Localization on Husimi Trees and its implications for Many-Body localization
• Critical Dynamics of the Anderson Transition on Small-World Graphs