Many-body localization in one dimension as a dynamical renormalization group fixed point

Abstract

We formulate a dynamical real space renormalization group approach to describe the time evolution of a random spin-1/2 chain, or interacting fermions, initialized in a state with fixed particle positions. Within this approach we identify a many-body localized state of the chain as a dynamical infinite randomness fixed point. Near this fixed point our method becomes asymptotically exact, allowing analytic calculation of time dependent quantities. In particular we explain the striking universal features in the growth of the entanglement seen in recent numerical simulations: unbounded logarithmic growth delayed by a time inversely proportional to the interaction strength. The particle number fluctuations by contrast exhibit much slower growth as log(log(t)) indicating blocked particle transport. Lack of true thermalization in the long time limit is attributed to an infinite set of approximate integrals of motion revealed in the course of the RG flow, which become asymptotically exact conservation laws at the fixed point. Hence we identify the many-body localized state with an emergent generalized Gibbs ensemble.

6 pages, 1 figure

References in corpus (6)

• Thermalization and its mechanism for generic isolated quantum systems
• Localization of interacting fermions at high temperature
• Many body localization in Heisenberg XXZ magnet in a random field
• Absence of Thermalization in Nonintegrable Systems
• Quantum Quenches, Thermalization and Many-Body Localization
• Towards measuring Entanglement Entropies in Many Body Systems

Cited by in corpus (303)

• Many body localization and thermalization in quantum statistical mechanics
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Many-body localization, thermalization, and entanglement
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Exploring the many-body localization transition in two dimensions
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• Quantum entanglement in condensed matter systems
• Operator Spreading in Random Unitary Circuits
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Experimental Observation of a Generalized Gibbs Ensemble
• Many-body localization: an introduction and selected topics
• Universal slow growth of entanglement in interacting strongly disordered systems
• Many-body localization in a disordered quantum Ising chain
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• Many-body localization in periodically driven systems
• Universal dynamics and renormalization in many body localized systems
• Area laws in a many-body localized state and its implications for topological order
• Localization protected quantum order
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Coupling Identical 1D Many-Body Localized Systems
• 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
• Ultracold atoms out of equilibrium
• Extended slow dynamical regime close to the many-body localization transition
• Universal properties of many-body delocalization transitions
• Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems
• The Ergodic Side of the Many-Body Localization Transition
• Constructing local integrals of motion in the many-body localized phase
• Exact Excited States of Non-Integrable Models
• Out-of-Time-Order Correlation for Many-Body Localization
• Signatures of Many-Body Localization in a Controlled Open Quantum System
• Avalanches and many-body resonances in many-body localized systems
• Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems
• Many-body Localization with Dipoles
• Stark many-body localization
• Many-body localization characterized from a one-particle perspective
• Slow scrambling in disordered quantum systems
• Classification of Interacting Topological Floquet Phases in One Dimension
• Prethermalization and universal dynamics in near-integrable quantum systems
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• Review: Local Integrals of Motion in Many-Body Localized systems
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
• The Hilbert-glass transition: new universality of temperature-tuned many-body dynamical quantum criticality
• Rare region effects and dynamics near the many-body localization transition
• Dynamical quantum phase transitions in random spin chains
• Glassy quantum dynamics in translation invariant fracton models
• A theory of many-body localization in periodically driven systems
• Low-frequency conductivity in many-body localized systems
• Quantum quenches in the many-body localized phase
• Spectral features of a many-body localized system weakly coupled to a heat bath
• Measurement-induced phase transition: A case study in the non-integrable model by density-matrix renormalization group calculations
• Interferometric probes of many-body localization
• Out-of-time-order correlations in many-body localized and thermal phases
• Dynamics at the Many-Body Localization Transition
• Explicit Local Integrals of Motion for the Many-Body Localized State
• Many-body mobility edge in a mean-field quantum spin glass
• Quasi Many-body Localization in Translation Invariant Systems
• Griffiths effects and slow dynamics in nearly many-body localized systems
• Absence of true localization in many-body localized phases
• Experimental observation of a phase transition in the evolution of many-body systems with dipolar interactions
• Chiral Floquet Phases of Many-body Localized Bosons
• Many-Body Localization in the Age of Classical Computing
• Many body localization in the presence of a single particle mobility edge
• Quantum Disentangled Liquids
• Finding matrix product state representations of highly-excited eigenstates of many-body localized Hamiltonians
• Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization
• Entanglement spreading in a many-body localized system
• Symmetry constraints on many-body localization
• Many-body localization due to random interactions
• Measuring the Renyi entropy of a two-site Fermi-Hubbard model on a trapped ion quantum computer
• Thermodynamic Equilibrium as a Symmetry of the Schwinger-Keldysh Action
• Quantum criticality of hot random spin chains
• Time Evolution of Many-Body Localized Systems with the Flow Equation Approach
• Fixed points of Wegner-Wilson flows and many-body localization
• Dynamical Stability of a Many-body Kapitza Pendulum
• Purification and many-body localization in cold atomic gases
• Many-body localization in disorder-free systems: the importance of finite-size constraints
• Strong Disorder RG approach - a short review of recent developments
• Quantum correlations and entanglement in far-from-equilibrium spin systems
• Signatures of the many-body localization transition in the dynamics of entanglement and bipartite fluctuations
• Many-body critical phase: extended and nonthermal
• The Many-Body localization transition in the Hilbert space
• Efficient variational diagonalization of fully many-body localized Hamiltonians
• Many-body localization in infinite chains
• Universal properties of many-body localization transitions in quasiperiodic systems
• Asymptotic quantum many-body localization from thermal disorder
• Many-body localization, symmetry, and topology
• Spin transport of weakly disordered Heisenberg chain at infinite temperature
• Typicality approach to the optical conductivity in thermal and many-body localized phases
• Can many-body localization persist in the presence of long-range interactions or long-range hopping?
• Many-body localization beyond eigenstates in all dimensions
• Total correlations of the diagonal ensemble herald the many-body localization transition
• Entanglement spectroscopy on a quantum computer
• Dynamics and Transport at the Threshold of Many-Body Localization
• Dynamical conductivity and its fluctuations along the crossover to many-body localization
• Many-body delocalisation as symmetry breaking
• Many-body localization and quantum ergodicity in disordered long-range Ising models
• Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain
• Marginal Anderson localization and many body delocalization
• Particle-hole symmetry, many-body localization, and topological edge modes
• Many-body mobility edge due to symmetry-constrained dynamics and strong interactions
• Signatures of many-body localisation in a system without disorder and the relation to a glass transition
• A mean-field theory of nearly many-body localized metals
• Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group
• The many-body localized phase of the quantum random energy model
• Finding purifications with minimal entanglement
• One-particle density matrix characterization of many-body localization
• Excited-state entanglement and thermal mutual information in random spin chains
• Spectral tensor networks for many-body localization
• Out-of-Time-Order Correlation in Marginal Many-Body Localized Systems
• Eigenstate phase transitions and the emergence of universal dynamics in highly excited states
• Many-body localization in Fock-space: a local perspective
• Explicit construction of local conserved operators in disordered many-body systems
• A semi-classical limit for the many-body localization transition
• Stretched exponential decay of Majorana edge modes in many-body localized Kitaev chains under dissipation
• Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems
• Accessing many-body localized states through the Generalized Gibbs Ensemble
• Restoring coherence via aperiodic drives in a many-body quantum system
• The effect of $SU(2)$ symmetry on many-body localization and thermalization
• How does a locally constrained quantum system localize?
• Quantum quenches and many-body localization in the thermodynamic limit
• Resonance-induced growth of number entropy in strongly disordered systems
• Effect of long-range hopping and interactions on entanglement dynamics and many-body localization
• Entanglement dynamics of a many-body localized system coupled to a bath
• Localization and symmetry breaking in the quantum quasiperiodic Ising glass
• Discrete time crystal enabled by Stark many-body localization
• Localization Properties of the XY Spin Chain. A review of mathematical results with an eye toward Many-Body Localization
• Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions
• Integrals of motion for one-dimensional Anderson localized systems
• Encoding the structure of many-body localization with matrix product operators
• Construction of exact constants of motion and effective models for many-body localized systems
• Integrable and chaotic dynamics of spins coupled to an optical cavity
• Entanglement entropy of disordered quantum chains following a global quench
• Interpretable Machine Learning Study of Many-Body Localization Transition in Disordered Quantum Ising Spin Chains
• Topological and symmetry-enriched random quantum critical points
• Maximum refractive index of an atomic medium
• Universal dynamics of density correlations at the transition to many-body localized state
• Universal algebraic growth of entanglement entropy in many-body localized systems with power-law interactions
• Activating many-body localization in solids by driving with light
• Non-equilibrium quantum relaxation across a localization-delocalization transition
• How periodic driving heats a disordered quantum spin chain
• Entanglement growth in many-body localized systems with long-range interactions
• Energy diffusion in the ergodic phase of a many body localizable spin chain
• Exploring many-body localization in quantum systems coupled to an environment via Wegner-Wilson flows
• Entanglement in a dephasing model and many-body localization
• Self-consistent approach to many-body localization and subdiffusion
• Many-body dynamics in long-range hopping model in the presence of correlated and uncorrelated disorder
• A self-consistent Hartree-Fock approach to Many-Body Localization
• Exploring many body localization and thermalization using semiclassical method
• Many-Body-Localization Transition : strong multifractality spectrum for matrix elements of local operators
• Subdiffusion in a 1D Anderson insulator with random dephasing: Finite-size scaling, Griffiths effects, and possible implications for many-body localization
• Loschmidt Echo in Many-Body Localized Phase
• Strong disorder renormalization group primer and the superfluid-insulator transition
• Many-Body Localization : construction of the emergent local conserved operators via block real-space renormalization
• Exploring one particle orbitals in large Many-Body Localized systems
• Probing many-body localization by excited-state VQE
• Entanglement in non-equilibrium steady states and many-body localization breakdown in a current driven system
• Entanglement scaling of excited states in large one-dimensional many-body localized systems
• Phenomenology of anomalous transport in disordered one-dimensional systems
• Many-body localization in large systems: Matrix-product-state approach
• Entanglement and the Sign Structure of Quantum States
• Distinctive response of many-body localized systems to strong electric field
• Mobility edge of Stark many-body localization
• Superdiffusive transport of energy in one-dimensional metals
• Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries
• Unusual area-law violation in random inhomogeneous systems
• Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains
• Many-body localization in Ising models with random long-range interactions
• Non-Abelian symmetries and disorder: a broad non-ergodic regime and anomalous thermalization
• Integrable spin chains with random interactions
• Understanding analog quantum simulation dynamics in coupled ion-trap qubits
• Anyonic self-induced disorder in a stabilizer code: quasi-many body localization in a translational invariant model
• Algebraic Localization from Power-Law Interactions in Disordered Quantum Wires
• Many Body Localization Transition in the strong disorder limit : entanglement entropy from the statistics of rare extensive resonances
• Unitary long-time evolution with quantum renormalization groups and artificial neural networks
• Probing Many-Body Localization by Spin Noise Spectroscopy
• $1/f^{\alpha }$ noise and generalized diffusion in random Heisenberg spin systems
• Nonequilibrium quench dynamics in quantum quasicrystals
• Mobility edge in long-range interacting many-body localized systems
• Quench dynamics of one-dimensional interacting bosons in a disordered potential: Elastic dephasing and critical speeding-up of thermalization
• A uniform area law for the entanglement of eigenstates in the disordered XY chain
• Eigenstate phases with finite on-site non-Abelian symmetry
• Family-Vicsek dynamical scaling and Kardar-Parisi-Zhang-like superdiffusive growth of surface roughness in a driven one-dimensional quasiperiodic model
• Disordered XYZ Spin Chain Simulations using the Spectrum Bifurcation Renormalization Group
• Many-body ground state localization and coexistence of localized and extended states in an interacting quasiperiodic system
• Comparing many-body localization lengths via non-perturbative construction of local integrals of motion
• Entanglement and thermodynamic entropy in a clean many-body-localized system
• Spin-mediated particle transport in the disordered Hubbard model
• Homogeneous Floquet time crystal from weak ergodicity breaking
• Disorder-assisted excitation localization in chirally coupled quantum emitters
• String order parameters for 1d Floquet Symmetry Protected Topological Phases
• Signatures of multifractality in a periodically driven interacting Aubry-André model
• Double light-cone dynamics establish thermal states in integrable 1D Bose gases
• Multifractal Orthogonality Catastrophe in 1D Random Quantum Critical Points
• Optimal Quench for Distance-Independent Entanglement and Maximal Block Entropy
• Quantum scars in spin-1/2 isotropic Heisenberg clusters
• Thermalization and many-body localization in systems under dynamic nuclear polarization
• A toy model for anomalous transport and Griffiths effects near the Many-Body Localization transition
• Remanent magnetization: signature of Many-Body Localization in quantum antiferromagnets
• Local integrals of motion in the two-site Anderson-Hubbard model
• Many body localization proximity effects in platforms of coupled spins and bosons
• Probability distribution of the entanglement across a cut at an infinite-randomness fixed point
• Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field
• Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
• Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model
• Supersymmetric Many-Body Systems from Partial Symmetries: Integrability, Localization and Scrambling
• Entanglement scaling in fermion chains with a localization-delocalization transition and inhomogeneous modulations
• Strong Disorder Real-Space Renormalization for the Many-Body-Localized phase of random Majorana models
• Macroscopic Length Correlations in Non-Equilibrium Systems and Their Possible Realizatons
• Entanglement dynamics in critical random quantum Ising chain with perturbations
• Density-Matrix Renormalization Group study of Many-Body Localization in Floquet Eigenstates
• Generalized Dyson model: nature of zero mode and its implication in dynamics
• Entanglement entropy of the long-range Dyson hierarchical model
• Linear and logarithmic entanglement production in an interacting chaotic system
• Analyzing many-body localization with a quantum computer
• Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization
• Observational entropic study of Anderson localization
• Subspace restricted thermalization in a correlated-hopping model with strong Hilbert space fragmentation characterized by irreducible strings
• Evolution of the magnetization after a local quench in the critical transverse-field Ising chain
• Quantum criticality in the 2d quasiperiodic Potts model
• Many-body localized phase of bosonic dipoles in a tilted optical lattice
• Localization of Rung Pairs in Hard-core Bose-Hubbard Ladder
• Quantum information spreading in random spin chains
• Random Transverse Field Spin-Glass Model on the Cayley tree : phase transition between the two Many-Body-Localized Phases
• Many-Body Localization from Dynamical Gauge Fields
• Observation of anisotropy-independent magnetization dynamics in spatially disordered Heisenberg spin systems
• Strong Disorder Renormalization for the dynamics of Many-Body-Localized systems : iterative elimination of the fastest degree of freedom via the Floquet expansion
• Glassy dynamics of the one-dimensional Mott insulator excited by a strong terahertz pulse
• Quantum dynamics with an ensemble of Hamiltonians
• Boltzmann transport theory for many body localization
• Universal crossover from ground state to excited-state quantum criticality
• Instability of localization in translation-invariant systems
• Perturbative instability of non-ergodic phases in non-Abelian quantum chains
• Efficient Classical Shadow Tomography through Many-body Localization Dynamics
• Thermalization propagation front and robustness against avalanches in localized systems
• Extensive entropy from unitary evolution
• Phenomenology of many-body localization in bond-disordered spin chains
• Quantum Coherence in Ergodic and Many-Body Localized Systems
• Nonequilibrium dynamical renormalization group: Dynamical crossover from weak to infinite randomness in the transverse-field Ising chain
• Critical quench dynamics of random quantum spin chains: Ultra-slow relaxation from initial order and delayed ordering from initial disorder
• Dynamics of Negativity of a Wannier-Stark Many-Body Localized System Coupled to a Bath
• Localization of spin waves in disordered quantum rotors
• Many-Body Localization: Concepts and Simple Models
• Single spin probe of Many-Body Localization
• Polaron in a non-abelian Aubry-André-Harper model with \textit{p}-wave superfluidity
• Interaction-Induced Weakening of Localization in Few-Particle Disordered Heisenberg Chains
• Dynamic scaling of the restoration of rotational symmetry in Heisenberg quantum antiferromagnets
• Renormalization group analysis of near-field induced dephasing of optical spin waves in an atomic medium
• Entanglement entropy and localization in disordered quantum chains
• Investigating disordered many-body system with entanglement in momentum space
• Finite-size subthermal regime in disordered SU(N)-symmetric Heisenberg chains
• One-dimensional L{é}vy Quasicrystal
• Even and odd normalized zero modes in random interacting Majorana models respecting the Parity $P$ and the Time-Reversal-Symmetry $T$
• Dynamical potentials for non-equilibrium quantum many-body phases
• Edge mode locality in perturbed symmetry protected topological order
• Characterizing the many-body localization transition through correlations
• Interplay of Anderson localization and quench dynamics
• Healing of Defects in Random Antiferromagnetic Spin Chains
• Renormalization-Group Analysis of the Many-Body Localization Transition in the Random-Field XXZ Chain
• Many-body localization with mobility edges
• Correlations generated from high-temperature states: nonequilibrium dynamics in the Fermi-Hubbard model
• An exactly solvable model for Dynamic Nuclear polarization
• Transverse-spin correlations of the random transverse-field Ising model
• Tracking locality in time evolution of disordered systems
• Renormalization view on resonance proliferation between many-body localized phases
• Contour-time approach to the disordered Bose-Hubbard model in the strong coupling regime
• Persistent Ballistic Entanglement Spreading with Optimal Control in Quantum Spin Chains
• Slow relaxation and sensitivity to disorder in trapped lattice fermions after a quench
• Accessing eigenstate spin-glass order from reduced density matrices
• Adding boundary terms to Anderson localized Hamiltonians leads to unbounded growth of entanglement
• Efficient simulation of many-body localized systems
• Scaling analysis and renormalization group on the mobility edge in the quantum random energy model
• The eigenstate distribution fluctuation from thermal to localized transitions
• Coherent backscattering in the Fock space of ultracold bosonic atoms
• Bloch oscillations in interacting systems driven by a time-dependent magnetic field
• Many-body critical phase in a quasiperiodic chain and dynamical Widom lines in Fock space properties
• Thermal avalanches in isolated many-body localized systems
• Sub-ballistic operator growth in spin chains with heavy-tailed random fields
• Symmetry- and energy-resolved entanglement dynamics in a disordered Bose-Hubbard model
• Slowest and Fastest Information Scrambling in the Strongly Disordered XXZ Model
• The Sub-Exponential Critical Slowing Down at Floquet Time Crystal Phase Transition
• Construction of Many-Body-Localized Models where all the eigenstates are Matrix-Product-States
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Signatures of many-body localization and metastability by weak perturbation
• Probing the many-body localized spin-glass phase through quench dynamics
• A theory of quasiballistic spin transport
• Measurement-Induced Phase Transition in a Disordered XX Spin Chain: A Real-Space Renormalization Group Study
• Time-dependent Real-space Renormalization-Group Approach: application to an adiabatic random quantum Ising model
• A journey into localization, integrability and thermalization
• Random cubic graph embedded in a hypercube: Entanglement spectrum and many-body localization
• Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Ground State Properties
• Diagnostics of Hilbert space fragmentation, freezing transition, and its effects in the family of quantum East models involving varying range of constraints
• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport
• Nonequilibrium localization and the interplay between disorder and interactions
• Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Excited States and Finite Temperature Properties
• Beyond the imbalance: site-resolved dynamics probing resonances in many-body localization
• Theoretical study on thermalization in isolated quantum systems
• Mechanism of defect formation in the quantum annealing of the random transverse-field Ising chain
• Localization dynamics in a centrally coupled system