Extended slow dynamical regime close to the many-body localization transition

Abstract

Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to $L=28$ sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth $S(t)\propto t^{1/z}$ with a disorder-dependent exponent $z\ge 1$, in contrast with the pure ballistic growth $z=1$ of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance $\mathcal{I}(t)\propto t^{-\zeta }$ with a continuously varying disorder-dependent exponent $\zeta$, vanishing at the transition. This provides a clear experimental signature for detecting this non-conventional regime.

5 pages, 3 figures

References in corpus (15)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Real time evolution using the density matrix renormalization group
• Many-body localization edge in the random-field Heisenberg chain
• Many body localization in Heisenberg XXZ magnet in a random field
• Integrals of motion in the Many-Body localized phase
• 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
• Constructing local integrals of motion in the many-body localized phase
• Absence of Thermalization in Nonintegrable Systems
• Ergodicity breaking in a model showing many-body localization
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• Quantum quenches in the many-body localized phase
• Purification and many-body localization in cold atomic gases

Cited by in corpus (259)

• Quantum entanglement in condensed matter systems
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Many-body localization: an introduction and selected topics
• Quantum chaos challenges many-body localization
• The Ergodic Side of the Many-Body Localization Transition
• Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system
• Signatures of Many-Body Localization in a Controlled Open Quantum System
• Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems
• Multifractal Scalings across the Many-Body Localization Transition
• Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems
• Observation of many-body localization in a one-dimensional system with single-particle mobility edge
• Thouless time analysis of Anderson and many-body localization transitions
• Review: Local Integrals of Motion in Many-Body Localized systems
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
• Rare region effects and dynamics near the many-body localization transition
• Quantum critical behavior at the many-body-localization transition
• Anomalous thermalization in ergodic systems
• Evidence for unbounded growth of the number entropy in many-body localized phases
• How a small quantum bath can thermalize long localized chains
• Many-body localization and delocalization in large quantum chains
• Many-body delocalization as a quantum avalanche
• Information propagation in isolated quantum systems
• Thouless energy and multifractality across the many-body localization transition
• Challenges to observation of many-body localization
• Absence of true localization in many-body localized phases
• Griffiths effects and slow dynamics in nearly many-body localized systems
• Dynamics of strongly interacting systems: From Fock-space fragmentation to Many-Body Localization
• Sub-ballistic growth of Rényi entropies due to diffusion
• Many body localization and thermalization: insights from the entanglement spectrum
• Analytically solvable renormalization group for the many-body localization transition
• Many-Body Localization in the Age of Classical Computing
• Mobility edge and intermediate phase in one-dimensional incommensurate lattice potentials
• Kosterlitz-Thouless scaling at many-body localization phase transitions
• Observation of energy resolved many-body localization
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
• Dynamics of entanglement and transport in 1D systems with quenched randomness
• Long tail distributions near the many body localization transition
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Density propagator for many-body localization: finite size effects, transient subdiffusion, and exponential decay
• From Anderson localization on Random Regular Graphs to Many-Body localization
• Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
• Many-body localization due to random interactions
• Time Evolution of Many-Body Localized Systems with the Flow Equation Approach
• Scaling Theory of Entanglement at the Many-Body Localization Transition
• Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance and out-of-time-ordered correlator
• Extended nonergodic states in disordered many-body quantum systems
• Level statistics across the many--body localization transition
• Return probability for the Anderson model on the random regular graph
• Time dynamics with matrix product states: Many-body localization transition of large systems revisited
• Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
• Delocalized Glassy Dynamics and Many Body Localization
• Many-body localization in infinite chains
• The Many-Body localization transition in the Hilbert space
• Renormalization-group study of the many-body localization transition in one dimension
• Bimodal entanglement entropy distribution in the many-body localization transition
• Is there slow particle transport in the MBL phase?
• Absence of full many-body localization in the disordered Hubbard chain
• Many-body localization, symmetry, and topology
• Machine Learning Many-Body Localization: Search for the Elusive Nonergodic Metal
• Many-body delocalization dynamics in long Aubry-André quasiperiodic chains
• Spin transport of weakly disordered Heisenberg chain at infinite temperature
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Butterfly effect in interacting Aubry-Andre model: thermalization, slow scrambling, and many-body localization
• Slow dynamics and strong finite-size effects in many-body localization with random and quasi-periodic potential
• Anomalous transport in the Aubry-André-Harper model in isolated and open systems
• Dynamics and Transport at the Threshold of Many-Body Localization
• Dynamical conductivity and its fluctuations along the crossover to many-body localization
• Many-Body Localization in Spin Chain Systems with Quasiperiodic Fields
• Many-body localization of bosons in optical lattices
• 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
• Driving induced many-body localization
• Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
• Noise-induced subdiffusion in strongly localized quantum systems
• Dynamical Manifestations of Quantum Chaos: Correlation Hole and Bulge
• Model of level statistics for disordered interacting quantum many-body systems
• Multifractality and its role in anomalous transport in the disordered XXZ spin-chain
• Detecting a many-body mobility edge with quantum quenches
• Slow many-body delocalization beyond one dimension
• One-particle density matrix characterization of many-body localization
• Finding purifications with minimal entanglement
• Signatures of many-body localisation in the dynamics of two-sites entanglement
• Eigenstate correlations around many-body localization transition
• Phenomenology of the Prethermal Many-Body Localized Regime
• Multiscale entanglement clusters at the many-body localization phase transition
• Many-body localization and delocalization from the perspective of Integrals of Motion
• Eigenstate phase transitions and the emergence of universal dynamics in highly excited states
• Counting local integrals of motion in disordered spinless-fermion and Hubbard chains
• Many-body localization in a quasiperiodic Fibonacci chain
• Learning phase transitions from dynamics
• Thermal inclusions: how one spin can destroy a many-body localized phase
• Apparent slow dynamics in the ergodic phase of a driven many-body localized system without extensive conserved quantities
• From ergodic to non-ergodic chaos in Rosenzweig-Porter model
• Multifractal metal in a disordered Josephson Junction Array
• Percolation in Fock space as a proxy for many-body localisation
• Stability of many-body localization in Floquet systems
• Domain-wall melting as a probe of many-body localization
• Spin subdiffusion in disordered Hubbard chain
• Flow towards diagonalization for Many-Body-Localization models : adaptation of the Toda matrix differential flow to random quantum spin chains
• Unusual wave-packet spreading and entanglement dynamics in non-Hermitian disordered many-body systems
• Many-body localization caused by temporal disorder
• Density correlations and transport in models of many-body localization
• Spin-charge separation and many-body localization
• Observation of many-body Fock space dynamics in two dimensions
• Transition to a many-body localized regime in a two-dimensional disordered quantum dimer model
• Universality in Anderson localization on random graphs with varying connectivity
• Emergent hydrodynamics in non-equilibrium quantum systems
• Characterizing the many-body localization transition through the entanglement spectrum
• Anomalous dynamics in the ergodic side of the Many-Body Localization transition and the glassy phase of Directed Polymers in Random Media
• Distribution of the Ratio of Consecutive Level Spacings for Different Symmetries and Degrees of Chaos
• Sub-diffusive Thouless time scaling in the Anderson model on random regular graphs
• Diffusive transport in a quasiperiodic Fibonacci chain: absence of many-body localization at small interactions
• Asymmetry in energy versus spin transport in certain interacting, disordered systems
• Universal dynamics of density correlations at the transition to many-body localized state
• Entanglement in a dephasing model and many-body localization
• Energy diffusion in the ergodic phase of a many body localizable spin chain
• Phenomenology of spectral functions in disordered spin chains at infinite temperature
• Self-consistent approach to many-body localization and subdiffusion
• Dephasing enhanced spin transport in the ergodic phase of a many-body localizable system
• One-particle-density-matrix occupation spectrum of many-body localized states after a global quench
• Many-body localization transition in large quantum spin chains: The mobility edge
• Many-Body-Localization Transition : strong multifractality spectrum for matrix elements of local operators
• Many-body localization for randomly interacting bosons
• Subdiffusion in a 1D Anderson insulator with random dephasing: Finite-size scaling, Griffiths effects, and possible implications for many-body localization
• Local integrals of motion and the quasiperiodic many-body localization transition
• Exploring one particle orbitals in large Many-Body Localized systems
• Equilibration time in many-body quantum systems
• Anomalous thermalization and transport in disordered interacting Floquet systems
• Statistics of correlation functions in the random Heisenberg chain
• Investigating many-body mobility edges in isolated quantum systems
• Phenomenology of anomalous transport in disordered one-dimensional systems
• The internal clock of many-body delocalization
• Drude weight fluctuations in many-body localized systems
• Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
• Stabilizer entropy in non-integrable quantum evolutions
• Discrete disorder models for many-body localization
• Matrix product states approaches to operator spreading in ergodic quantum systems
• Scaling up the Anderson transition in random-regular graphs
• Quasi-Many-Body Localization of Interacting Fermions with Long-Range Couplings
• Stark many-body localization transitions in superconducting circuits
• Entanglement dynamics in the many-body Hatano-Nelson model
• Many-body localization phase in a spin-driven chiral multiferroic chain
• Spin-catalyzed hopping conductivity in disordered strongly interacting quantum wires
• Unitary long-time evolution with quantum renormalization groups and artificial neural networks
• Many-Body Localization in a finite-range Sachdev-Ye-Kitaev model
• Glassy Dynamics from Quark Confinement: Atomic Quantum Simulation of Gauge-Higgs Model on Lattice
• Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain
• Critical dynamics at the Anderson localization mobility edge
• Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder
• Decay of spin-spin correlations in disordered quantum and classical spin chains
• Probing many-body localization in a disordered quantum dimer model on the honeycomb lattice
• Dynamical Scaling of Surface Roughness and Entanglement Entropy in Disordered Fermion Models
• Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium
• Signatures of chaos and thermalization in the dynamics of many-body quantum systems
• Catching thermal avalanches in the disordered XXZ model
• Delocalized charge carriers in strongly disordered t-J model
• Reduced-basis approach to many-body localization
• Many-body delocalization from embedded thermal inclusion
• Many-body localization and enhanced non-ergodic sub-diffusive regime in the presence of random long-range interactions
• The Timescales of Quantum Breaking
• Dephasing in strongly disordered interacting quantum wires
• Multipartite-Entanglement Dynamics in Regular-to-Ergodic Transition: a Quantum-Fisher-Information approach
• From eigenstate to Hamiltonian: Prospects for ergodicity and localization
• Power-law entanglement growth from typical product states
• Sub-diffusive phases in open clean long-range systems
• Scaling properties of a spatial one-particle density-matrix entropy in many-body localized systems
• Particle fluctuations and the failure of simple effective models for many-body localized phases
• Many-body localization transition in a frustrated XY chain
• Spin transport in disordered long-range interacting spin chain
• 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
• Stability of electric-field-driven MBL in an interacting long range hopping model
• A toy model for anomalous transport and Griffiths effects near the Many-Body Localization transition
• Complete many-body localization in the t-J model caused by random magnetic field
• Many-Body-Localization Transition : sensitivity to twisted boundary conditions
• Beyond many-body localized states in a spin-disordered Hubbard model with pseudo-spin symmetry
• Relaxation at different length-scales in models of many-body localization
• Remanent magnetization: signature of Many-Body Localization in quantum antiferromagnets
• Many-body localization as a percolation phenomenon
• Probability transport on the Fock space of a disordered quantum spin chain
• From Ergodicity to Many-Body Localization in a One-Dimensional Interacting Non-Hermitian Stark System
• Many-body localization transition through pairwise correlations
• Many-Body Mobility Edge in Quantum Sun models
• Does a distinct quasi many-body localized phase exist? A numerical study of a translationally invariant system in the thermodynamic limit
• Slow dynamics of a mobile impurity interacting with an Anderson insulator
• Subdiffusion in one-dimensional Hamiltonian chains with sparse interactions
• Information-Theoretic Memory Scaling in the Many-Body Localization Transition
• Generalized Dyson model: nature of zero mode and its implication in dynamics
• Tensor networks demonstrate the robustness of localization and symmetry protected topological phases
• Boundary driven Heisenberg-chain in the long-range interacting regime: Robustness against far from equilibrium effects
• Slow diffusion and Thouless localization criterion in modulated spin chains
• Many-body localization in one dimensional optical lattice with speckle disorder
• Dynamics of the one-dimensional Anderson insulator coupled to various bosonic baths
• Linear and logarithmic entanglement production in an interacting chaotic system
• Diffusion in the Anderson model in higher dimensions
• Benchmarking a novel efficient numerical method for localized 1D Fermi-Hubbard systems on a quantum simulator
• Many-body localization with synthetic gauge fields in disordered Hubbard chains
• Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport
• Large scale behavior of the energy spectra of the quantum random antiferromagnetic Ising chain with mixed transverse and longitudinal fields
• On intermediate statistics across many-body localization transition
• Many-Body Localization: Transitions in Spin Models
• Ergodic inclusions in many body localized systems
• Einstein relation for a driven disordered quantum chain in subdiffusive regime
• Strong Disorder Renormalization for the dynamics of Many-Body-Localized systems : iterative elimination of the fastest degree of freedom via the Floquet expansion
• Eigenstate properties of the disordered Bose-Hubbard chain
• Boltzmann transport theory for many body localization
• Multifractality in the interacting disordered Tavis-Cummings model
• The connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains
• Strongly disordered Anderson insulator chains with generic two-body interaction
• Thermalization propagation front and robustness against avalanches in localized systems
• Many-body localization crossover is sharper in quasiperiodic spin chains
• Resistivity and its fluctuations in disordered many-body systems: from chains to planes
• Decay of density waves in coupled one-dimensional many-body-localized systems
• Many-Body-Localization : Strong Disorder perturbative approach for the Local Integrals of Motion
• Open-system spin transport and operator weight dissipation in spin chains
• Finite-size prethermalization at the chaos-to-integrable crossover
• Bounding the finite-size error of quantum many-body dynamics simulations
• Localization and integrability breaking in weakly interacting Floquet circuits
• Interaction-Induced Weakening of Localization in Few-Particle Disordered Heisenberg Chains
• Many-body localization regime for cavity induced long-range interacting models
• Effects of auto-correlated disorder on the dynamics in the vicinity of the many-body localization transition
• Many-body localization of 1D disordered impenetrable two-component fermions
• Localization of fermions in coupled chains with identical disorder
• Semiclassical bounds on dynamics of two-dimensional interacting disordered fermions
• Emergent statistical bubble localization in a Z2 lattice gauge theory
• Characterizing the many-body localization transition through correlations
• Dynamical potentials for non-equilibrium quantum many-body phases
• Many-body localized to ergodic transitions in a system with correlated disorder
• Operator Growth in Disordered Spin Chains: Indications for the Absence of Many-Body Localization
• Probing prethermal nonergodicity through measurement outcomes of monitored quantum dynamics
• Modelling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains
• Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder
• Many-body localization of ${\mathbb{Z}}_3$ Fock parafermions
• Nonequilibrium many-body quantum dynamics: from full random matrices to real systems
• Disorder effects in the ${\mathbb{Z}}_3$ Fock parafermion chain
• Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space
• Many-body localization in the infinite-interaction limit and the discontinuous eigenstate phase transition
• Finite size scaling for the Many-Body-Localization Transition : finite-size-pseudo-critical points of individual eigenstates
• Logarithmic growth of local entropy and total correlations in many-body localized dynamics
• Quench dynamics of two component dipolar fermions subject to a quasiperiodic potential
• The eigenstate distribution fluctuation from thermal to localized transitions
• Universal properties of single particle excitations across the many-body localization transition
• Disordered impenetrable two-component fermions in one dimension
• Memory effects in the density-wave imbalance in delocalized disordered systems
• Stochastic and long-distance level spacing statistics in many-body localization
• Extended nonergodic regime and spin subdiffusion in disordered SU(2)-symmetric Floquet systems
• Spin and energy diffusion vs. subdiffusion in disordered spin chains
• Symmetry- and energy-resolved entanglement dynamics in a disordered Bose-Hubbard model
• Delocalization in a partially disordered interacting many-body system
• Anomalous diffusion in quantum system driven by heavy-tailed stochastic processes
• Classical periodic trajectories and quantum scars in many-spin systems
• Relaxation mechanisms in a disordered system with the Poisson level statistics
• Late-time universal distribution functions of observables in one-dimensional many-body quantum systems
• Beyond the imbalance: site-resolved dynamics probing resonances in many-body localization
• Local density of states and scattering rates across the many-body localization transition
• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport