Recent progress in many-body localization

Abstract

This article is a brief introduction to the rapidly evolving field of many-body localization. Rather than giving an in-depth review of the subject, our aspiration here is simply to introduce the problem and its general context, outlining a few directions where notable progress has been achieved in recent years. We hope that this will prepare the readers for the more specialized articles appearing in the forthcoming dedicated volume of Annalen der Physik, where these developments are discussed in more detail.

Invited overview article for the Special Volume of Annalen der Physik on Many-Body Localization

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• Many-body localization: an introduction and selected topics
• Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approach
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
• Simulating quantum many-body dynamics on a current digital quantum computer
• Multifractal Scalings across the Many-Body Localization Transition
• From Bloch Oscillations to Many Body Localization in Clean Interacting Systems
• Spectral statistics in spatially extended chaotic quantum many-body systems
• Colloquium: Quantum and Classical Discrete Time Crystals
• 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
• Can we study the many-body localisation transition?
• Aspects of non-equilibrium in classical and quantum systems: slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics
• Adiabatic eigenstate deformations as a sensitive probe for quantum chaos
• Non-Hermitian disorder in two-dimensional optical lattices
• Signatures of rare states and thermalization in a theory with confinement
• Quantum Slow Relaxation and Metastability due to Dynamical Constraints
• Many-body localization in a non-Hermitian quasi-periodic system
• Measurement-induced entanglement transitions in many-body localized systems
• Shift-invert diagonalization of large many-body localizing spin chains
• Koopman-von Neumann Approach to Quantum Simulation of Nonlinear Classical Dynamics
• Quantum many-body scars from virtual entangled pairs
• Disorder in quantum many-body systems
• Return probability for the Anderson model on the random regular graph
• Many-body localization transition with power-law interactions: Statistics of eigenstates
• Confinement and lack of thermalization after quenches in the bosonic Schwinger model
• Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
• Coherent and dissipative dynamics at quantum phase transitions
• The Many-Body localization transition in the Hilbert space
• Universal properties of many-body localization transitions in quasiperiodic systems
• Is there slow particle transport in the MBL phase?
• Flat-band many-body localization and ergodicity breaking in the Creutz ladder
• Critical behavior at the localization transition on random regular graphs
• Many-body localization, symmetry, and topology
• Many-body delocalization dynamics in long Aubry-André quasiperiodic chains
• Many-Body Flatband Localization
• Two critical localization lengths in the Anderson transition on random graphs
• Dynamical Localization in ${\mathbb{Z}}_2$ Lattice Gauge Theories
• Sub-diffusion in the Anderson model on random regular graph
• Exact Floquet quantum many-body scars under Rydberg blockade
• Transport properties across the many-body localization transition in quasiperiodic and random systems
• Many-body localization of bosons in optical lattices
• Reinforcement learning for autonomous preparation of Floquet-engineered states: Inverting the quantum Kapitza oscillator
• 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
• Anderson transition on the Bethe lattice: an approach with real energies
• Localization with random time-periodic quantum circuits
• Stark many-body localization: Evidence for Hilbert-space shattering
• Multifractality and its role in anomalous transport in the disordered XXZ spin-chain
• Slow many-body delocalization beyond one dimension
• Finding purifications with minimal entanglement
• Eigenstate correlations around many-body localization transition
• Random Matrix Ensemble for the Level Statistics of Many-Body Localization
• Multiscale entanglement clusters at the many-body localization phase transition
• Absence of dynamical localization in interacting driven systems
• Learning phase transitions from dynamics
• Many-body localization in a fragmented Hilbert space
• Many-body localization in a quasiperiodic Fibonacci chain
• Avalanche induced co-existing localised and thermal regions in disordered chains
• Apparent slow dynamics in the ergodic phase of a driven many-body localized system without extensive conserved quantities
• Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
• Derivation of exact flow equations from the self-consistent parquet relations
• Operator and entanglement growth in non-thermalizing systems: many-body localization and the random singlet phase
• Percolation in Fock space as a proxy for many-body localisation
• Absence of Thermalization in Finite Isolated Interacting Floquet Systems
• Chaos and quantum scars in Bose-Josephson junction coupled to a bosonic mode
• Transition to a many-body localized regime in a two-dimensional disordered quantum dimer model
• Orthogonal Quantum Many-body Scars
• Anomalous dynamics in the ergodic side of the Many-Body Localization transition and the glassy phase of Directed Polymers in Random Media
• Complex Quantum Networks: a Topical Review
• Localization in spin chains with facilitation constraints and disordered interactions
• Asymmetry in energy versus spin transport in certain interacting, disordered systems
• Universal algebraic growth of entanglement entropy in many-body localized systems with power-law interactions
• Energy transport in a disordered spin chain with broken U(1) symmetry: Diffusion, subdiffusion, and many-body localization
• Diagnosing entanglement dynamics in noisy and disordered spin chains via the measurement-induced steady-state entanglement transition
• Neural network setups for a precise detection of the many-body localization transition: finite-size scaling and limitations
• Operator content of entanglement spectra after global quenches in the transverse field Ising chain
• Correlations and dynamical quantum phase transitions in an interacting topological insulator
• Subdiffusion in a 1D Anderson insulator with random dephasing: Finite-size scaling, Griffiths effects, and possible implications for many-body localization
• Exploring one particle orbitals in large Many-Body Localized systems
• Anomalous thermalization and transport in disordered interacting Floquet systems
• Extended flat-bands, entanglement and topological properties in a Creutz ladder
• Statistics of correlation functions in the random Heisenberg chain
• Bounds on Energy Absorption and Prethermalization in Quantum Systems with Long-Range Interactions
• Many-body localization in large systems: Matrix-product-state approach
• Disorder-free localization in a simple $U(1)$ lattice gauge theory
• Hilbert-space fragmentation, multifractality, and many-body localization
• Transport in Stark Many Body Localized Systems
• Phenomenology of anomalous transport in disordered one-dimensional systems
• Investigating many-body mobility edges in isolated quantum systems
• 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
• Many-body dynamical phase transition in quasi-periodic potential
• Numerical evidence for many-body localization in two and three dimensions
• Symmetry enhanced boundary qubits at infinite temperature
• Discrete disorder models for many-body localization
• Drive-induced many-body localization and coherent destruction of Stark many-body localization
• Integrable spin chains with random interactions
• Condensation transition and ensemble inequivalence in the Discrete Nonlinear Schrödinger Equation
• Real-Time Dynamics of Typical and Untypical States in Non-Integrable Systems
• Symmetry restoration and quantum Mpemba effect in many-body localization systems
• Algebraic Localization from Power-Law Interactions in Disordered Quantum Wires
• Hubbard Models for Quasicrystalline Potentials
• Stark many-body localization transitions in superconducting circuits
• Many-body localization as a large family of localized ground states
• Interaction-Driven Instabilities in the Random-Field XXZ Chain
• From ETH to algebraic relaxation of OTOCs in systems with conserved quantities
• Adaptive-weighted tree tensor networks for disordered quantum many-body systems
• Coherence, entanglement and quantumness in closed and open systems with conserved charge, with an application to many-body localisation
• Out of equilibrium Phase Diagram of the Quantum Random Energy Model
• Mobility edge in long-range interacting many-body localized systems
• Loschmidt amplitude spectrum in dynamical quantum phase transitions
• Mean field theory of failed thermalizing avalanches
• Entanglement renormalization for disordered systems
• Local integrals of motion detection of localization-protected topological order
• Eigenstate entanglement between quantum chaotic subsystems: universal transitions and power laws in the entanglement spectrum
• Probing many-body localization in a disordered quantum dimer model on the honeycomb lattice
• Local Integrals of Motion for Topologically Ordered Many-Body Localized Systems
• Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations
• Remnants of Anderson localization in pre-thermalization induced by white noise
• Localized dynamics following a quantum quench in a non-integrable system: An example on the sawtooth ladder
• Motif magnetism and quantum many-body scars
• Many-body localization and enhanced non-ergodic sub-diffusive regime in the presence of random long-range interactions
• Exact Mobility edges and topological Anderson insulating phase in a slowly varying quasiperiodic model
• Disorder-free localization in quantum walks
• Many-body localization transition in a frustrated XY chain
• Dynamical route to ergodicity and quantum scarring in kicked coupled top
• Fully localized and partially delocalized states in the tails of Erdös-Rényi graphs in the critical regime
• Spin transport in disordered long-range interacting spin chain
• Many-body localization transition from flatband fine-tuning
• Floquet-induced localization in long-range many-body systems
• Localization persisting under aperiodic driving
• Random matrix theory for quantum and classical metastability in local Liouvillians
• Entanglement in coupled kicked tops with chaotic dynamics
• Spectral statistics of a minimal quantum glass model
• 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
• Thermal and dissipative effects on the heating transition in a driven critical system
• Dynamics of Many-Body Delocalization in the Time-dependent Hartree-Fock Approximation
• 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
• High-frequency Expansion for Floquet Prethermal Phases with Emergent Symmetries: Application to Time Crystals and Floquet Engineering
• Many body localization proximity effects in platforms of coupled spins and bosons
• The Fock-space landscape of many-body localisation
• Quantum Jamming: Critical Properties of a Quantum Mechanical Perceptron
• Classification of symmetry-protected topological phases in two-dimensional many body-localized systems
• Information-Theoretic Memory Scaling in the Many-Body Localization Transition
• Many-body localization in the Fock space of natural orbitals
• Quantum jumps in driven-dissipative disordered many-body systems
• Freezing transition in particle-conserving East model
• Tensor networks demonstrate the robustness of localization and symmetry protected topological phases
• Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation
• Classification of symmetry-protected topological many-body localized phases in one dimension
• Signatures of Many-Body Localization in the Dynamics of Two-Level Systems in Glasses
• Quantum information spreading in random spin chains with topological order
• ${\mathcal{L}}^2$ localization landscape for highly-excited states
• Eigenvector Correlations Across the Localisation Transition in non-Hermitian Power-Law Banded Random Matrices
• Many-body localization of zero modes
• Hilbert space fragmentation at the origin of disorder-free localization in the lattice Schwinger model
• Ergodic inclusions in many body localized systems
• Initial State Dependent Dynamics Across Many-body Localization Transition
• Parallel Quantum Algorithm for Hamiltonian Simulation
• Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization
• Many-Body Localization: Transitions in Spin Models
• Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
• Pair localization in dipolar systems with tunable positional disorder
• Instability of localization in translation-invariant systems
• Many-body-localization induced protection of symmetry-protected topological order in a XXZ spin model
• Many-body-localization protection of eigenstate topological order in two dimensions
• The connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains
• Stochastic strong zero modes and their dynamical manifestations
• Response of a quantum disordered spin system to a local periodic drive
• Memories of initial states and density imbalance in dynamics of interacting disordered systems
• A microscopically motivated renormalization scheme for the MBL/ETH transition
• Entanglement of a class of non-Gaussian states in disordered harmonic oscillator systems
• Quantum transport efficiency in noisy random-removal and small-world networks
• Signature of Generalized Gibbs Ensemble Deviation from Equilibrium: Negative Absorption Induced by a Local Quench
• Robustness of Stark many-body localization in the $J_1$-$J_2$ Heisenberg model
• Time dependence of few-body Förster interactions among ultracold Rydberg atoms
• Many-body localization in Landau level subbands
• Many-body localization of 1D disordered impenetrable two-component fermions
• Semiclassical simulations predict glassy dynamics for disordered Heisenberg models
• Duality between disordered nodal semimetals and systems with power-law hopping
• Schmidt gap in random spin chains
• Entanglement entropy and localization in disordered quantum chains
• From the Quantum Breakdown Model to the Lattice Gauge Theory
• Nonequilibrium quantum order at infinite temperature: spatiotemporal correlations and their generating functions
• Deformation of localized states and state transitions in systems of randomly hopping interacting fermions
• Many-body localized to ergodic transitions in a system with correlated disorder
• Anderson localisation in steady states of microcavity polaritons
• Projected ensemble in a system with conserved charges with local support
• Construction of Many-Body Eigenstates with Displacement Transformations
• Coulomb blockade in a non-thermalized quantum dot
• Universal distributions of overlaps from generic dynamics in quantum many-body systems
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Dynamical potentials for non-equilibrium quantum many-body phases
• Fate of dissipative hierarchy of timescales in the presence of unitary dynamics
• Many-body localization of ${\mathbb{Z}}_3$ Fock parafermions
• Random-matrix perspective on many-body entanglement with a finite localization length
• Glassy dynamics in strongly anharmonic chains of oscillators
• Intensity pseudo-localized phase in the glassy random laser
• Tunable Anderson Localization of Dark States
• Imperfect Many-Body Localization in Exchange-Disordered Isotropic Spin Chains
• Quantum Many-Body Scars in Few-Body Dipole-Dipole Interactions
• Topology and many-body localization
• Fermionic phases and their transitions induced by competing finite-range interactions
• Many-Body Localization in Translational Invariant Diamond Ladders with Flat Bands
• Finite-size scaling analysis of localization transitions in the disordered two-dimensional Bose-Hubbard model within the fluctuation operator expansion method
• Coherent charge and spin oscillations induced by local quenches in nanowires with spin-orbit coupling
• Logarithmic growth of local entropy and total correlations in many-body localized dynamics
• Adding boundary terms to Anderson localized Hamiltonians leads to unbounded growth of entanglement
• Localization and interactions in topological and non-topological bands in two dimensions
• Chaos enhancement in large-spin chains
• Protecting coherence from the environment via Stark many-body localization in a Quantum-Dot Simulator
• Trends of information backflow in disordered spin chains
• The eigenstate distribution fluctuation from thermal to localized transitions
• Quantum measurements and equilibration: the emergence of objective outcomes via entropy maximisation
• Generic eigenstate preparation via measurement-based purification
• Anomalous Diffusion, Prethermalization, and Particle Binding in an Interacting Flat Band System
• Characterizing dynamical criticality of many-body localization transitions from the Fock-space perspective
• Entanglement dynamics and eigenstate correlations in strongly disordered quantum many-body systems
• Quantum metamorphism
• Anatomy of localisation protected quantum order on Hilbert space
• Many-body critical phase in a quasiperiodic chain and dynamical Widom lines in Fock space properties
• Logarithmic entanglement lightcone from eigenstate correlations in the many-body localised phase
• Thermal avalanches in isolated many-body localized systems
• Multifractality in high-dimensional graphs induced by correlated radial disorder
• Disordered impenetrable two-component fermions in one dimension
• Numerical study of the temperature dependence of the NMR relaxation rate across the superfluid-Bose glass transition in one dimension
• Memory effects in the density-wave imbalance in delocalized disordered systems
• Anomalous relaxation of density waves in a ring-exchange system
• Dynamical Evolution of Entanglement in Disordered Oscillator Systems
• An eigensystem approach to Anderson localization for multi-particle systems
• Anderson localisation in two dimensions: insights from Localisation Landscape Theory, exact diagonalisation, and time-dependent simulations
• Disorder free many-body localization transition in two quasiperiodically coupled Heisenberg spin chains
• State preparation and evolution in quantum computing: a perspective from Hamiltonian moments
• Onset of universality in the dynamical mixing of a pure state
• The Wishart--Rosenzweig--Porter random matrix ensemble
• Krylov-space anatomy and spread complexity of a disordered quantum spin chain
• Random cubic graph embedded in a hypercube: Entanglement spectrum and many-body localization
• Numerical and quantum simulation of a quantum disentangled liquid
• Localization-delocalization effects of a delocalizing dissipation on disordered XXZ spin chains
• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree
• Fluctuation driven transitions in localized insulators: Intermittent metallicity and path chaos precede delocalization
• 2D Anderson Localization and KPZ sub-Universality Classes : sensitivity to boundary conditions and insensitivity to symmetry classes
• From eigenstate thermalization to hydrodynamic transport in correlated metals
• Quantum transitions, ergodicity, and quantum scars in the coupled top model
• Quantum Lyapunov exponents and complex spacing ratios: two measures of Dissipative Quantum Chaos
• Many-body localization in a tilted potential in two dimensions
• Heat percolation in many-body flatband localizing systems
• Many-body localization in a slowly varying potential
• Efficient detection of localization transitions using predictability
• Adaptive quantum dynamics with the time-dependent variational Monte Carlo method
• Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping
• Universal fluctuations of localized two interacting particles in one dimension
• Effective metal-insulator non-equilibrium quantum phase transition
• Scrambling dynamics across a thermalization-localization quantum phase transition
• Quantum Markov chain Monte Carlo method with programmable quantum simulators