Local conservation laws and the structure of the many-body localized states

Abstract

We construct a complete set of local integrals of motion that characterize the many-body localized (MBL) phase. Our approach relies on the assumption that local perturbations act locally on the eigenstates in the MBL phase, which is supported by numerical simulations of the random-field XXZ spin chain. We describe the structure of the eigenstates in the MBL phase and discuss the implications of local conservation laws for its non-equilibrium quantum dynamics. We argue that the many-body localization can be used to protect coherence in the system by suppressing relaxation between eigenstates with different local integrals of motion.

4.5 pages, 2 figures; v2: published version

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• Localization, multifractality, and many-body localization in periodically kicked quasiperiodic lattices
• Eigenstate Thermalization and Representative States on Subsystems
• Massively parallel implementation and approaches to simulate quantum dynamics using Krylov subspace techniques
• Probing spin hydrodynamics on a superconducting quantum simulator
• A toy model for anomalous transport and Griffiths effects near the Many-Body Localization transition
• Many-Body-Localization Transition : sensitivity to twisted boundary conditions
• A scalable numerical approach to the solution of the Dyson equation for the non-equilibrium single-particle Green's function
• Floquet-induced localization in long-range many-body systems
• Transport in the non-ergodic extended phase of interacting quasiperiodic systems
• Quantum quenches in isolated quantum glasses out of equilibrium
• Configuration-Controlled Many-Body Localization and the Mobility Emulsion
• Local integrals of motion in the two-site Anderson-Hubbard model
• Beyond many-body localized states in a spin-disordered Hubbard model with pseudo-spin symmetry
• Remanent magnetization: signature of Many-Body Localization in quantum antiferromagnets
• Localization of Extended Quantum Objects
• Approximating observables on eigenstates of large many-body localized systems
• Exact projector Hamiltonian, local integrals of motion, and many-body localization with topological order
• Statistically related many-body localization in the one-dimensional anyon Hubbard model
• Multifractality and Fock-space localization in many-body localized states: one-particle density matrix perspective
• Relaxation at different length-scales in models of many-body localization
• Hilbert-space correlations beyond multifractality and bipartite entanglement in many-body localised systems
• Nucleation of ergodicity by a single mobile impurity in supercooled insulators
• The Fock-space landscape of many-body localisation
• Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
• Bridging quantum many-body scar and quantum integrability in Ising chains with transverse and longitudinal fields
• Many-body physics with ultracold plasmas: Quenched randomness and localization
• Eigenstate localization in a many-body quantum system
• Many body localization proximity effects in platforms of coupled spins and bosons
• Probability transport on the Fock space of a disordered quantum spin chain
• Many-body localization as a percolation phenomenon
• Many-Body Mobility Edge in Quantum Sun models
• Strong Disorder Real-Space Renormalization for the Many-Body-Localized phase of random Majorana models
• A Quantum Breakdown Model: from Many-body Localization to Chaos with Scars
• Entanglement dynamics in critical random quantum Ising chain with perturbations
• Explicit construction of quasi-conserved local operator of translationally invariant non-integrable quantum spin chain in prethermalization
• Classification of symmetry-protected topological phases in two-dimensional many body-localized systems
• Classical and quantum systems: transport due to rare events
• Ergodic and localized regions in quantum spin glasses on the Bethe lattice
• Density-Matrix Renormalization Group study of Many-Body Localization in Floquet Eigenstates
• Ultraslow Growth of Number Entropy in an l-bit Model of Many-Body Localization
• Loschmidt echo singularities as dynamical signatures of strongly localized phases
• Supersymmetric Many-Body Systems from Partial Symmetries: Integrability, Localization and Scrambling
• Anomalous localization at the boundary of an interacting topological insulator
• Stable many-body localization under random continuous measurements in the no-click limit
• Subdiffusion in one-dimensional Hamiltonian chains with sparse interactions
• Boundary driven Heisenberg-chain in the long-range interacting regime: Robustness against far from equilibrium effects
• Classification of symmetry-protected topological many-body localized phases in one dimension
• Tensor networks demonstrate the robustness of localization and symmetry protected topological phases
• Many-body localization in one dimensional optical lattice with speckle disorder
• Tower of quantum scars in a partially many-body localized system
• Slow diffusion and Thouless localization criterion in modulated spin chains
• Nonstabilizerness dynamics in many-body localized systems
• On the possibility of many-body localization in a doped Mott insulator
• Studying many-body localization in exchange-coupled electron spin qubits using spin-spin correlations
• Charge and spin-specific local integrals of motion in a disordered Hubbard model
• Disorder enhanced quantum many-body scars in Hilbert crystals
• Many-body localization with synthetic gauge fields in disordered Hubbard chains
• Mobility edge of the two dimensional Bose-Hubbard model
• From Ansätze to Z-gates: a NASA View of Quantum Computing
• Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization
• Identifying Correlation Clusters in Many-Body Localized Systems
• Spatio-temporal heterogeneity of entanglement in many-body localized systems
• Mott, Floquet, and the response of periodically driven Anderson insulators
• Localization of a mobile impurity interacting with an Anderson insulator
• Analyzing many-body localization with a quantum computer
• A stabilization mechanism for many-body localization in two dimensions
• Breaking the chains: extreme value statistics and localization in random spin chains
• Many-body localized phase of bosonic dipoles in a tilted optical lattice
• Inverted many-body mobility edge in a central qudit problem
• Hilbert space fragmentation at the origin of disorder-free localization in the lattice Schwinger model
• Dynamics and Asymptotics of Correlations in a Many-Body Localized System
• Combating quasiparticle poisoning with multiple Majorana fermions in a periodically-driven quantum wire
• Quantum coherence controls the nature of equilibration in coupled chaotic systems
• Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system
• Entanglement Entropy in Excited States of the Quantum Lifshitz Model
• Quantum information spreading in random spin chains
• Ergodic inclusions in many body localized systems
• Signatures of many-body localization of quasiparticles in a flat band superconductor
• Quantum supremacy and quantum phase transitions
• Universal crossover from ground state to excited-state quantum criticality
• Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking
• Strong Disorder Renormalization for the dynamics of Many-Body-Localized systems : iterative elimination of the fastest degree of freedom via the Floquet expansion
• Pair localization in dipolar systems with tunable positional disorder
• Tower of two-dimensional scar states in a localized system
• Statistics of systemwide correlations in the random-field XXZ chain: Importance of rare events in the many-body localized phase
• Gumbel statistics for entanglement spectra of many-body localized eigenstates
• Instability of localization in translation-invariant systems
• Level repulsion exponent $\beta$ for Many-Body Localization Transitions and for Anderson Localization Transitions via Dyson Brownian Motion
• Strongly correlated photon transport in nonlinear photonic lattice with disorder: Probing signatures of the localization transition
• Eigenstate properties of the disordered Bose-Hubbard chain
• Quench-induced delocalization
• 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
• Energy dependence of localization with interactions and disorder: The generalized inverse participation ratio of an ensemble of two-site Anderson-Hubbard systems
• Harnessing symmetry-protected topological order for quantum memories
• Perturbative instability of non-ergodic phases in non-Abelian quantum chains
• Bound state and Localization of excitation in many-body open systems
• Structural properties of local integrals of motion across the many-body localization transition via a fast and efficient method for their construction
• Many body localization transition with correlated disorder
• Exact many-body scars based on pairs or multimers in a chain of spinless fermions
• The connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains
• Interacting Local Topological Markers: A one-particle density matrix approach for characterizing the topology of interacting and disordered states
• Efficient Classical Shadow Tomography through Many-body Localization Dynamics
• Step Heat Profile in Localized Chains
• Ergodicity breaking and Localization of the Nicolai supersymmetric fermion lattice model
• Floquet Engineering of Hilbert Space Fragmentation in Stark Lattices
• Interaction-Induced Characteristic Length in Strongly Many-Body Localized Systems
• Thermalization propagation front and robustness against avalanches in localized systems
• Decay of density waves in coupled one-dimensional many-body-localized systems
• Many-body localization crossover is sharper in quasiperiodic spin chains
• Krylov complexity in quantum many-body scars of spin-1 models
• Dynamics of pattern-loaded fermions in bichromatic optical lattices
• Response of a quantum disordered spin system to a local periodic drive
• A microscopically motivated renormalization scheme for the MBL/ETH transition
• Coupled identical localized fermionic chains with quasi-random disorder
• Scale Invariant Entanglement Negativity at the Many-Body Localization Transition
• Experimentally accessible witnesses of many-body localisation
• Observation of ergodicity breaking and quantum many-body scars in spinor gases
• Many-Body-Localization : Strong Disorder perturbative approach for the Local Integrals of Motion
• Dynamical many-body delocalization transition of a Tonks gas in a quasi-periodic driving potential
• Detecting emergent continuous symmetries at quantum criticality
• Measuring out quasi-local integrals of motion from entanglement
• Finite-size prethermalization at the chaos-to-integrable crossover
• Localization in the constrained quantum annealing of graph coloring
• Clean two-dimensional Floquet time-crystal
• Quantum Coherence in Ergodic and Many-Body Localized Systems
• Localization and integrability breaking in weakly interacting Floquet circuits
• Localization in the Discrete Non-Linear Schrödinger Equation and geometric properties of the microcanonical surface
• Slow propagation in some disordered quantum spin chains
• Conserved Quantities from Entanglement Hamiltonian
• Dynamics of Negativity of a Wannier-Stark Many-Body Localized System Coupled to a Bath
• Phenomenology of many-body localization in bond-disordered spin chains
• Interaction-Induced Weakening of Localization in Few-Particle Disordered Heisenberg Chains
• Space-time generalization of mutual information
• Quantum Adiabatic Doping with Incommensurate Optical Lattices
• Probing Hilbert space fragmentation and the block inverse participation ratio
• Gutzwiller projection for exclusion of holes: Application to strongly correlated Ionic Hubbard Model and Binary Alloys
• Lattice Hamiltonians and Stray Interactions Within Quantum Processors
• Single spin probe of Many-Body Localization
• Entanglement Measures in a Nonequilibrium Steady State: Exact Results in One Dimension
• Fate of Algebraic Many-Body Localization under driving
• Cat states carrying long-range correlations in the many-body localized phase
• Many-body localization of 1D disordered impenetrable two-component fermions
• Bounding the resources for thermalizing many-body localized systems
• Statistics of orthogonality catastrophe events in localised disordered lattices
• The Ergodicity Landscape of Quantum Theories
• Finite-size subthermal regime in disordered SU(N)-symmetric Heisenberg chains
• Localization of fermions in coupled chains with identical disorder
• Disorder-induced spin-charge separation in the 1-D Hubbard model
• Effective realization of random magnetic fields in compounds with large single-ion anisotropy
• Topologically ordered time crystals
• Real-time dynamics of 1D and 2D bosonic quantum matter deep in the many-body localized phase
• Projected ensemble in a system with conserved charges with local support
• Swapping Floquet time crystal
• Prolonging a discrete time crystal by quantum-classical feedback
• Probing localization properties of many-body Hamiltonians via an imaginary vector potential
• Renormalization-Group Analysis of the Many-Body Localization Transition in the Random-Field XXZ Chain
• Deformation of localized states and state transitions in systems of randomly hopping interacting fermions
• Edge mode locality in perturbed symmetry protected topological order
• Many-body localization and delocalization dynamics in the thermodynamic limit
• Construction of Many-Body Eigenstates with Displacement Transformations
• Out-of-equilibrium dynamics of repulsive Fermi gases in quasi-periodic potentials: a Density Functional Theory study
• Emergent statistical bubble localization in a Z2 lattice gauge theory
• Even and odd normalized zero modes in random interacting Majorana models respecting the Parity $P$ and the Time-Reversal-Symmetry $T$
• Hamiltonian Dynamics of a Sum of Interacting Random Matrices
• Characterizing the many-body localization transition through correlations
• Boosting entanglement growth of many-body localization by superpositions of disorder
• Contour-time approach to the disordered Bose-Hubbard model in the strong coupling regime
• Imperfect Many-Body Localization in Exchange-Disordered Isotropic Spin Chains
• Tracking locality in time evolution of disordered systems
• Correlations generated from high-temperature states: nonequilibrium dynamics in the Fermi-Hubbard model
• Reviving product states in the disordered Heisenberg chain
• Many-body localization of ${\mathbb{Z}}_3$ Fock parafermions
• Interacting spinning fermions with quasi-random disorder
• Quantum Many-Body Scars in Few-Body Dipole-Dipole Interactions
• Atypical energy eigenstates in the Hubbard chain and quantum disentangled liquids
• Operator Growth in Disordered Spin Chains: Indications for the Absence of Many-Body Localization
• Scar-induced imbalance in staggered Rydberg ladders
• Many-body localization with mobility edges
• Quantum Inverse Freezing and Mirror-Glass Order
• Finite steady-state current defies non-Hermitian many-body localization
• Response to a local quench of a system near many body localization transition
• Stability and Dynamics of Many-Body Localized Systems Coupled to Small Bath
• Equilibration and "Thermalization'' in the Adapted Caldeira-Leggett model
• Topology and many-body localization
• Flat-band full localization and symmetry-protected topological phase on bilayer lattice systems
• An exactly solvable model for Dynamic Nuclear polarization
• Renormalization view on resonance proliferation between many-body localized phases
• Perturbative Analysis of Quasi-periodic Patterning of Transmon Quantum Computers: Enhancement of Many-Body Localization
• Controlling quantum many-body systems using reduced-order modelling
• Finite-size scaling analysis of localization transitions in the disordered two-dimensional Bose-Hubbard model within the fluctuation operator expansion method
• Many-body localization in the infinite-interaction limit and the discontinuous eigenstate phase transition
• Entanglement dynamics and eigenstate correlations in strongly disordered quantum many-body systems
• Protecting Quantum Information via Many-Body Dynamical Localization
• Quench dynamics of two component dipolar fermions subject to a quasiperiodic potential
• Robustness of the Floquet many-body localized phase in the presence of a smooth and a non-smooth drive
• Finite size scaling for the Many-Body-Localization Transition : finite-size-pseudo-critical points of individual eigenstates
• Quantum Circuits Reproduce Experimental Two-dimensional Many-body Localization Transition Point
• Slow melting of a disordered quantum crystal
• Extensive Long-Range Entanglement at Finite Temperatures from a Nonequilibrium Bias
• Adding boundary terms to Anderson localized Hamiltonians leads to unbounded growth of entanglement
• Characterizing dynamical criticality of many-body localization transitions from the Fock-space perspective
• Protecting coherence from the environment via Stark many-body localization in a Quantum-Dot Simulator
• Many-Body Localization Transition, Temporal Fluctuations of the Loschmidt Echo, and Scrambling
• Logarithmic light cone, slow entanglement growth, and quantum memory
• Spin correlation functions and quasiparticle decay
• Information Dynamics in a Model with Hilbert Space Fragmentation
• Quantum metamorphism
• Efficient simulation of many-body localized systems
• Scaling analysis and renormalization group on the mobility edge in the quantum random energy model
• Localized Fock Space Cages in Kinetically Constrained Models
• Disordered Haldane-Shastry model
• Quantum purification spectroscopy
• Detecting Many-Body-Localization Length with Cold Atoms
• Finding local integrals of motion in quantum lattice models in the thermodynamic limit
• Logarithmic entanglement lightcone from eigenstate correlations in the many-body localised phase
• Anatomy of localisation protected quantum order on Hilbert space
• Many-body localization in the droplet spectrum of the random XXZ quantum spin chain
• Multibody expansion of the local integrals of motion: How many pairs of particle-hole do we really need to describe the quasiparticles in the many-body localized phase?
• Quench dynamics of quasi-periodic systems exhibiting Rabi oscillations of two-level integrals of motion
• Spin and energy diffusion vs. subdiffusion in disordered spin chains
• Cooling Quantum Gases with Entropy Localization
• Localization and slow-thermalization in a cluster spin model
• Thermal avalanches in isolated many-body localized systems
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble
• Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath
• Partial projected ensembles and spatiotemporal structure of information scrambling
• Localization Lifetime of a Many-Body System with Periodic Constructed Disorder
• Symmetry- and energy-resolved entanglement dynamics in a disordered Bose-Hubbard model
• Construction of Many-Body-Localized Models where all the eigenstates are Matrix-Product-States
• Coherent backscattering in the Fock space of ultracold bosonic atoms
• Stochastic and long-distance level spacing statistics in many-body localization
• Localization detection based on quantum dynamics
• Sub-ballistic operator growth in spin chains with heavy-tailed random fields
• Thermal transport in disordered one-dimensional spin chains
• Characterizing the Many Body Localization Crossover as a Metal-Insulator Transition: Localization length from Polarization and Quantum Metric
• Slowest and Fastest Information Scrambling in the Strongly Disordered XXZ Model
• Coexistence of ergodic and non-ergodic behavior and level spacing statistics in a one-dimensional model of a flat band superconductor
• Circular Rosenzweig-Porter random matrix ensemble
• Probing the many-body localized spin-glass phase through quench dynamics
• Characterizing the parent Hamiltonian for a complete set of orthogonal wave functions: An inverse quantum problem
• Quasiconservation Laws and Suppressed Transport in Weakly Interacting Localized Models
• Phase transition from localization to chaos in classical many-body system
• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree
• 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
• Anderson localisation in two dimensions: insights from Localisation Landscape Theory, exact diagonalisation, and time-dependent simulations
• Universality in Non-Equilibrium Quantum Systems
• Anomalous Enhancement of Entanglement Entropy in Nonequilibrium Steady States Driven by Zero-Temperature Reservoirs
• Information scrambling and entanglement dynamics in Floquet Time Crystals
• Generalized Gibbs Ensemble from Eigenstate Entanglement Hamiltonian
• Scrambling dynamics across a thermalization-localization quantum phase transition
• Identifying mobility edge from finite temperature spectral form factor
• Logarithmic growth of operator entanglement in a clean non-integrable circuit
• Limitations of SVD-Based Diagnostics for Non-Hermitian Many-Body Localization with Time-Reversal Symmetry
• Robustness and Independence of the Eigenstates with respect to the Boundary Conditions across a Delocalization-Localization Phase Transition
• Constraint-induced breaking and restoration of ergodicity in spin-1 PXP models
• Non-Markovianity Benefits Quantum Dynamics Simulation
• Non-commutative Index of Measurement-only Entanglement Phase Transition
• Localization and melting of interfaces in the two-dimensional quantum Ising model
• Controlling discrete time crystals via single-site operations in zero-field diamond quantum simulators
• Crossover from Quantum Chaos to a Reversed Quantum Disentangled Liquid in a Disorder-Free Spin Ladder
• Beyond the imbalance: site-resolved dynamics probing resonances in many-body localization
• Interaction-induced long-time tail of a nonlinear ac absorption in a localized system: a relay-race mechanism
• Operator delocalization in disordered spin chains via exact MPO marginals
• Theoretical study on thermalization in isolated quantum systems
• Unified theory of local integrals of motion
• From Bose glass to many-body localization in a one-dimensional disordered Bose gas
• Coherently synchronized oscillations in many-body localization
• Loop Charges and Fragmentation in Pairwise Difference Conserving Circuits
• Thouless Energy Across Many-Body Localization Transition in Floquet Systems
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain
• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport
• Parity Cross-Resonance: A Multiqubit Gate
• Diagnosing chaos with projected ensembles of process tensors
• Quantum Markov chain Monte Carlo method with programmable quantum simulators
• Two-dimensional many-body localized systems coupled to a heat bath
• Emergent Thermalization Thresholds in Unitary Dynamics of Inhomogeneously Disordered Quantum Systems
• AC Conductivity Crossover in Localized Superconductors
• Observation of Localization Using a Noisy Quantum Computer
• Many-body localization and particle multioccupancy in the disordered Bose-Hubbard model
• Quantum Avalanches in ${\mathbb{Z}}_2$-preserving Interacting Ising Majorana Chain
• Many-body localization in a slowly varying potential
• Krylov complexity of many-body localization: Operator localization in Krylov basis
• Many-body spectral transitions through the lens of the variable-range SYK2 model
• Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath
• Local density of states and scattering rates across the many-body localization transition
• Fock-space geometry and strong correlations in many-body localized systems
• Pure states statistical mechanics: On its foundations and applications to quantum gravity