Many-Body Localization in the Age of Classical Computing

Abstract

Statistical mechanics provides a framework for describing the physics of large, complex many-body systems using only a few macroscopic parameters to determine the state of the system. For isolated quantum many-body systems, such a description is achieved via the eigenstate thermalization hypothesis (ETH), which links thermalization, ergodicity and quantum chaotic behavior. However, tendency towards thermalization is not observed at finite system sizes and evolution times in a robust many-body localization (MBL) regime found numerically and experimentally in the dynamics of interacting many-body systems at strong disorder. Although the phenomenology of the MBL regime is well-established, the central question remains unanswered: under what conditions does the MBL regime give rise to an MBL phase in which the thermalization does not occur even in the asymptotic limit of infinite system size and evolution time? This review focuses on recent numerical investigations aiming to clarify the status of the MBL phase, and it establishes the critical open questions about the dynamics of disordered many-body systems. Persistent finite size drifts towards ergodicity consistently emerge in spectral properties of disordered many-body systems, excluding naive single-parameter scaling hypothesis and preventing comprehension of the status of the MBL phase. The drifts are related to tendencies towards thermalization and non-vanishing transport observed in the dynamics of many-body systems, even at strong disorder. These phenomena impede understanding of microscopic processes at the ETH-MBL crossover. Nevertheless, the abrupt slowdown of dynamics with increasing disorder strength suggests the proximity of the MBL phase. This review concludes that the questions about thermalization and its failure in disordered many-body systems remain a captivating area open for further explorations.

75 pages, 14 figures, updated version

References in corpus (239)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The density-matrix renormalization group in the age of matrix product states
• Thermalization and its mechanism for generic isolated quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• Many body localization and thermalization in quantum statistical mechanics
• Theoretical perspective on the glass transition and amorphous materials
• Anderson Transitions
• Localization of interacting fermions at high temperature
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Real time evolution using the density matrix renormalization group
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Quantum trajectories and open many-body quantum systems
• Many-body localization in periodically driven systems
• Quantum Many-Body Scars and Weak Breaking of Ergodicity
• Integrals of motion in the Many-Body localized phase
• Spectral signatures of many-body localization with interacting photons
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Many-Body Localization in a Quasiperiodic System
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Non-standard Hubbard models in optical lattices: a review
• The randomized measurement toolbox
• Generalized Thermalization in an Integrable Lattice System
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
• 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
• Signatures of Many-Body Localization in a Controlled Open Quantum System
• Avalanches and many-body resonances in many-body localized systems
• Ergodicity breaking in a model showing many-body localization
• Entanglement entropy for the long range Ising chain
• Chaos, Complexity, and Random Matrices
• Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
• Quantum Many-Body Scars: A Quasiparticle Perspective
• Provably efficient machine learning for quantum many-body problems
• Slow scrambling in disordered quantum systems
• Strongly interacting bosons in a disordered optical lattice
• Operator space entanglement entropy in transverse Ising chain
• Anomalous thermalization in ergodic systems
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Matrix Product States for dynamical simulation of infinite chains
• Many-body localization dynamics from gauge invariance
• Colloquium: Quantum and Classical Discrete Time Crystals
• Quantum Many-Body Scar States with Emergent Kinetic Constraints and Finite-Entanglement Revivals
• How a small quantum bath can thermalize long localized chains
• Off-diagonal matrix elements of local operators in many-body quantum systems
• Quantum quenches in the many-body localized phase
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
• Entanglement asymmetry as a probe of symmetry breaking
• Can we study the many-body localisation transition?
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
• Challenges to observation of many-body localization
• Krylov complexity from integrability to chaos
• Absence of true localization in many-body localized phases
• Exact diagonalization: the Bose-Hubbard model as an example
• Markovian baths and quantum avalanches
• Krylov Localization and suppression of complexity
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling
• Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
• Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
• Rare thermal bubbles at the many-body localization transition from the Fock space point of view
• Eigenstate thermalization and quantum chaos in the Holstein polaron model
• From Anderson localization on Random Regular Graphs to Many-Body localization
• Stark many-body localization on a superconducting quantum processor
• Many-body localization due to random interactions
• Quantum Mutual Information as a Probe for Many-Body Localization
• Entanglement equipartition in critical random spin chains
• A constructive theory of the numerically accessible many-body localized to thermal crossover
• Purification and many-body localization in cold atomic gases
• Many body localization with long range interactions
• Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
• Eigenstate Thermalization Hypothesis and Free Probability
• Many-body localization in infinite chains
• Signatures of bath-induced quantum avalanches in a many-body--localized system
• Renormalization-group study of the many-body localization transition in one dimension
• Is there slow particle transport in the MBL phase?
• Rényi entropy of a line in two-dimensional Ising models
• Absence of full many-body localization in the disordered Hubbard chain
• Critical behavior at the localization transition on random regular graphs
• Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
• Can many-body localization persist in the presence of long-range interactions or long-range hopping?
• Critical properties of the Anderson localization transition and the high dimensional limit
• Many-body localization near the critical point
• Diffusive high-temperature transport in the one-dimensional Hubbard model
• Transport properties across the many-body localization transition in quasiperiodic and random systems
• Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos
• Many-body delocalisation as symmetry breaking
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Chaos and ergodicity across the energy spectrum of interacting bosons
• Thermalization of dilute impurities in one dimensional spin chains
• Stark many-body localization: Evidence for Hilbert-space shattering
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Coexistence of diffusive and ballistic transport in a simple spin ladder
• Eigenstate correlations around many-body localization transition
• Signatures of many-body localisation in the dynamics of two-sites entanglement
• Phenomenology of the Prethermal Many-Body Localized Regime
• Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo
• Explicit construction of local conserved operators in disordered many-body systems
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
• Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization
• Fermionic many-body localization for random and quasiperiodic systems in the presence of short- and long-range interactions
• Many-body localization of bosons in optical lattice: Dynamics in disorder-free potentials
• Eigenstate thermalization hypothesis through the lens of autocorrelation functions
• Finite temperature transport in disordered Heisenberg chains
• Percolation in Fock space as a proxy for many-body localisation
• Stability of many-body localization in Floquet systems
• Quantum quenches and many-body localization in the thermodynamic limit
• Local resonances and parametric level dynamics in the many-body localised phase
• Poisson to GOE transition in the distribution of the ratio of consecutive level spacings
• Resonance-induced growth of number entropy in strongly disordered systems
• Probing quantum correlations in many-body systems: a review of scalable methods
• Fock-space anatomy of eigenstates across the many-body localisation transition
• Entanglement dynamics of a many-body localized system coupled to a bath
• Incoherent transport induced by a single static impurity in a Heisenberg chain
• Superdiffusive Energy Transport in Kinetically Constrained Models
• Nonlinear current response of an isolated system of interacting fermions
• Observation of many-body Fock space dynamics in two dimensions
• Universality in Anderson localization on random graphs with varying connectivity
• Interaction-driven breakdown of dynamical localization in a kicked quantum gas
• Many-body localization in tilted and harmonic potentials
• Many-Body Localization in System with a Completely Delocalized Single-Particle Spectrum
• Universal dynamics of density correlations at the transition to many-body localized state
• Many-body localization in presence of cavity mediated long-range interactions
• Phenomenology of spectral functions in disordered spin chains at infinite temperature
• Unlimited growth of particle fluctuations in many-body localized phases
• Genuine many-body quantum scars along unstable modes in Bose-Hubbard systems
• Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
• Weak integrability breaking perturbations of integrable models
• Many-body localization for randomly interacting bosons
• Energy level dynamics across the many-body localization transition
• Constraints induced delocalization
• Local integrals of motion and the quasiperiodic many-body localization transition
• Resonant energy scales and local observables in the many-body localised phase
• Light cone tensor network and time evolution
• Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians
• Multifractality and self-averaging at the many-body localization transition
• Hilbert space shattering and disorder-free localization in polar lattice gases
• Simulation of quantum many-body dynamics with Tensor Processing Units: Floquet prethermalization
• Many-body resonances in the avalanche instability of many-body localization
• Higher-order level spacings in random matrix theory based on Wigner's conjecture
• Many-body localization in large systems: Matrix-product-state approach
• Critical behavior of the Anderson model on the Bethe lattice via a large-deviation approach
• Scaling of Fock-space propagator and multifractality across the many-body localization transition
• Coexistence of localization and transport in many-body two-dimensional Aubry-André models
• Detecting delocalization-localization transitions from full density distributions
• The internal clock of many-body delocalization
• Many-body localization in Ising models with random long-range interactions
• Statistical Bubble Localization with Random Interactions
• Scale-Invariant Survival Probability at Eigenstate Transitions
• Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
• Local Integrals of Motion in Quasiperiodic Many-Body Localized Systems
• Analysis of Localization Phenomena in Weakly Interacting Disordered Lattice Gases
• Topological order in random interacting Ising-Majorana chains stabilized by many-body localization
• Scale-invariant critical dynamics at eigenstate transitions
• Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain
• Mean field theory of failed thermalizing avalanches
• Localization challenges quantum chaos in the finite two-dimensional Anderson model
• Mobility edge in long-range interacting many-body localized systems
• Entanglement Growth and Minimal Membranes in $(d+1)$ Random Unitary Circuits
• Role of Fock-space correlations in many-body localization
• Guide to Exact Diagonalization Study of Quantum Thermalization
• Generalized thermalization in quantum-chaotic quadratic Hamiltonians
• A note on the quasiperiodic many-body localization transition in dimension $d>1$
• Stability of mobility edges in disordered interacting systems
• Catching thermal avalanches in the disordered XXZ model
• Signatures of a critical point in the many-body localization transition
• Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations
• On the Spectral Form Factor for Random Matrices
• Detecting ergodic bubbles at the crossover to many-body localization using neural networks
• Analytical and numerical study of uncorrelated disorder on a honeycomb lattice
• Many-body localization and enhanced non-ergodic sub-diffusive regime in the presence of random long-range interactions
• Restoring ergodicity in a strongly disordered interacting chain
• Ergodicity-to-localization transition on random regular graphs with large connectivity and in many-body quantum dots
• Propagation of Many-body Localization in an Anderson Insulator
• Probing the metallic energy spectrum beyond the Thouless energy scale using the singular value decomposition
• Dephasing in strongly disordered interacting quantum wires
• Particle fluctuations and the failure of simple effective models for many-body localized phases
• Scaling properties of a spatial one-particle density-matrix entropy in many-body localized systems
• Localization, multifractality, and many-body localization in periodically kicked quasiperiodic lattices
• Polynomial filter diagonalization of large Floquet unitary operators
• Distinguishing an Anderson Insulator from a Many-Body Localized phase through space-time snapshots with Neural Networks
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Long-range level correlations in quantum systems with finite Hilbert space dimension
• Lattice control of non-ergodicity in a polar lattice gas
• Many-Body-Localization Transition : sensitivity to twisted boundary conditions
• Dynamics of Many-Body Delocalization in the Time-dependent Hartree-Fock Approximation
• Nonlinear Response in Diffusive Systems
• Relaxation at different length-scales in models of many-body localization
• Normal weak eigenstate thermalization
• Many-body localization as a percolation phenomenon
• Ergodicity breaking with long range cavity induced quasiperiodic interactions
• Hilbert-space correlations beyond multifractality and bipartite entanglement in many-body localised systems
• Probability transport on the Fock space of a disordered quantum spin chain
• Slow dynamics of a mobile impurity interacting with an Anderson insulator
• Flow Equations for Disordered Floquet Systems
• Diffusion in the Anderson model in higher dimensions
• Emergent dipole moment conservation and subdiffusion in tilted chains
• Slow diffusion and Thouless localization criterion in modulated spin chains
• Chaos and subdiffusion in the infinite-range coupled quantum kicked rotors
• Entropy and Temperature in finite isolated quantum systems
• Localization of a mobile impurity interacting with an Anderson insulator
• Identifying Correlation Clusters in Many-Body Localized Systems
• Localization spectrum of a bath-coupled generalized Aubry-André model in the presence of interactions
• Absence of localization in interacting spin chains with a discrete symmetry
• Spatio-temporal heterogeneity of entanglement in many-body localized systems
• A stabilization mechanism for many-body localization in two dimensions
• Disordered Lieb-Robinson bounds in one dimension
• Multiple relaxation times in perturbed XXZ chain
• Many-Body Localization: Transitions in Spin Models
• Initial State Dependent Dynamics Across Many-body Localization Transition
• Breaking the chains: extreme value statistics and localization in random spin chains
• Quantum chaos and level dynamics
• 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
• Many-body localization proximity effect in two-species bosonic Hubbard model
• Structural properties of local integrals of motion across the many-body localization transition via a fast and efficient method for their construction
• Extensive entropy from unitary evolution
• Entanglement dynamics in U(1) symmetric hybrid quantum automaton circuits
• Resilient infinite randomness criticality for a disordered chain of interacting Majorana fermions
• Enhanced many-body localization in a kinetically constrained model
• Measuring out quasi-local integrals of motion from entanglement
• Many-body localization regime for cavity induced long-range interacting models
• Many-body localized to ergodic transitions in a system with correlated disorder
• Beyond Fermi's golden rule with the statistical Jacobi approximation
• Probing localization properties of many-body Hamiltonians via an imaginary vector potential
• Modelling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains
• Subdiffusive spin transport in disordered classical Heisenberg chains
• The role of interaction-induced tunneling in the dynamics of polar lattice bosons
• Screening the Coulomb interaction leads to a prethermal regime in two-dimensional bad conductors
• Imperfect Many-Body Localization in Exchange-Disordered Isotropic Spin Chains
• Dynamics of position disordered Ising spins with a soft-core potential
• Quantum Circuits Reproduce Experimental Two-dimensional Many-body Localization Transition Point
• Evidence from on-site atom number fluctuations for a quantum Berezinskii-Kosterlitz-Thouless transition in the one-dimensional Bose-Hubbard model

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