Ergodicity Breaking Transition in Finite Disordered Spin Chains

Abstract

We study disorder-induced ergodicity breaking transition in high-energy eigenstates of interacting spin-1/2 chains. Using exact diagonalization we introduce a cost function approach to quantitatively compare different scenarios for the eigenstate transition. We study ergodicity indicators such as the eigenstate entanglement entropy and the spectral level spacing ratio, and we consistently find that an (infinite-order) Kosterlitz-Thouless transition yields a lower cost function when compared to a finite-order transition. Interestingly, we observe that the transition point in finite systems exhibits nearly thermal properties, i.e., ergodicity indicators at the transition are close to the random matrix theory predictions.

References in corpus (111)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Localization of interacting fermions at high temperature
• Many-body localization, thermalization, and entanglement
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• The many-body localization phase transition
• Quantum many-body systems out of equilibrium
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Quantum many-body scars
• Exploring the many-body localization transition in two dimensions
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• 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
• Many-body localization in a quantum simulator with programmable random disorder
• Generalized Gibbs ensemble in integrable lattice models
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• On Many-Body Localization for Quantum Spin Chains
• Many-body localization in a disordered quantum Ising chain
• Eigenstate Thermalization Hypothesis
• Time evolution of local observables after quenching to an integrable model
• Breakdown of thermalization in finite one-dimensional systems
• Probing entanglement in a many-body-localized system
• Universal dynamics and renormalization in many body localized systems
• Integrals of motion in the Many-Body localized phase
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Area laws in a many-body localized state and its implications for topological order
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
• Localization protected quantum order
• Quantum chaos challenges many-body localization
• Stability and instability towards delocalization in MBL systems
• Theory of the many-body localization transition in one dimensional systems
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Generalized Thermalization in an Integrable Lattice System
• Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Universal properties of many-body delocalization transitions
• Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
• Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets
• Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
• Disorder-induced Localization in a Strongly Correlated Atomic Hubbard Gas
• Multifractal Scalings across the Many-Body Localization Transition
• A criterion for many-body localization-delocalization phase transition
• Two universality classes for the many-body localization transition
• Many-body localization characterized from a one-particle perspective
• Thouless time analysis of Anderson and many-body localization transitions
• Thermalization near integrability in a dipolar quantum Newton's cradle
• The Hilbert-glass transition: new universality of temperature-tuned many-body dynamical quantum criticality
• Spectral statistics across the many-body localization transition
• Quantum critical behavior at the many-body-localization transition
• Critical Properties of the Many-Body Localization Transition
• Evidence for unbounded growth of the number entropy in many-body localized phases
• Many-body localization and delocalization in large quantum chains
• Many-body delocalization as a quantum avalanche
• Eigenstate thermalization within isolated spin-chain systems
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Can we study the many-body localisation transition?
• A Measure of data-collapse for scaling
• Dynamics at the Many-Body Localization Transition
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Early breakdown of area-law entanglement at many-body delocalization transition
• Thouless energy and multifractality across the many-body localization transition
• Conductivity of disordered quantum lattice models at infinite temperature: Many-body localization
• Entanglement and matrix elements of observables in interacting integrable systems
• Analytically solvable renormalization group for the many-body localization transition
• Kosterlitz-Thouless scaling at many-body localization phase transitions
• Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
• Time evolution of a quantum many-body system: transition from integrability to ergodicity in thermodynamic limit
• Many body localization in the presence of a single particle mobility edge
• Many-body localization and thermalization in disordered Hubbard chains
• Long tail distributions near the many body localization transition
• Shift-invert diagonalization of large many-body localizing spin chains
• Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition
• Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis in a One-Dimensional Interacting Bose gas
• Quantum Mutual Information as a Probe for Many-Body Localization
• Scaling Theory of Entanglement at the Many-Body Localization Transition
• Level statistics across the many--body localization transition
• Fixed points of Wegner-Wilson flows and many-body localization
• Many-body localization phase transition: A simplified strong-randomness approximate renormalization group
• Onset of Floquet Thermalisation
• Exact localized and ballistic eigenstates in disordered chaotic spin ladders and the Fermi-Hubbard model
• Renormalization-group study of the many-body localization transition in one dimension
• Bimodal entanglement entropy distribution in the many-body localization transition
• Quantum quenches in disordered systems: Approach to thermal equilibrium without a typical relaxation time
• Many-body Localization Transition: Schmidt Gap, Entanglement Length & Scaling
• Fundamental Asymmetry in Quenches Between Integrable and Nonintegrable Systems
• Many-body localization beyond eigenstates in all dimensions
• Dynamical conductivity and its fluctuations along the crossover to many-body localization
• Quantum Quenches in the Luttinger model and its close relatives
• Finite size scaling bounds on many-body localized phase transitions
• Model of level statistics for disordered interacting quantum many-body systems
• Eigenstate thermalization hypothesis and integrals of motion
• Random Matrix Ensemble for the Level Statistics of Many-Body Localization
• Conductivity in a disordered one-dimensional system of interacting fermions
• Comment on "Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis"
• Statistics of correlation functions in the random Heisenberg chain
• Phenomenology of anomalous transport in disordered one-dimensional systems
• Critical behavior near the many-body localization transition in driven open systems
• Many-body localization of spinless fermions with attractive interactions in one dimension
• Thouless Energy Challenges Thermalization on the Ergodic Side of the Many-Body Localization Transition
• Many-Body Localization Landscape
• Decay of spin-spin correlations in disordered quantum and classical spin chains
• Breakdown of ergodicity in disordered U(1) lattice gauge theories
• Resistivity and its fluctuations in disordered many-body systems: from chains to planes

Cited by in corpus (145)

• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Quantum chaos challenges many-body localization
• Avalanches and many-body resonances in many-body localized systems
• Dynamical obstruction to localization in a disordered spin chain
• Polynomially filtered exact diagonalization approach to many-body localization
• Absence of true localization in many-body localized phases
• Markovian baths and quantum avalanches
• Many-Body Localization in the Age of Classical Computing
• From Anderson localization on Random Regular Graphs to Many-Body localization
• Universality in the onset of quantum chaos in many-body systems
• Signatures of bath-induced quantum avalanches in a many-body--localized system
• Many-body localization near the critical point
• Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain
• Thermalization of dilute impurities in one dimensional spin chains
• Universal spectral form factor for many-body localization
• Many-body localization of bosons in optical lattice: Dynamics in disorder-free potentials
• Stability of many-body localization in Floquet systems
• Resonance-induced growth of number entropy in strongly disordered systems
• Finite-Size scaling analysis of many-body localization transition in quasi-periodic spin chains
• Observation of many-body Fock space dynamics in two dimensions
• Universality in Anderson localization on random graphs with varying connectivity
• Many-body localization in tilted and harmonic potentials
• Phenomenology of spectral functions in disordered spin chains at infinite temperature
• Unlimited growth of particle fluctuations in many-body localized phases
• Many-body localization transition in large quantum spin chains: The mobility edge
• Constraints induced delocalization
• Local integrals of motion and the quasiperiodic many-body localization transition
• Non-Hermitian Stark Many-Body Localization
• Detecting delocalization-localization transitions from full density distributions
• The internal clock of many-body delocalization
• Delayed Thermalization in Mass-Deformed SYK
• Nonergodic dynamics in disorder-free potentials
• Extracting many body localization lengths with an imaginary vector potential
• Symmetry restoration and quantum Mpemba effect in many-body localization systems
• Scale-Invariant Survival Probability at Eigenstate Transitions
• Stark many-body localization transitions in superconducting circuits
• Interaction-Driven Instabilities in the Random-Field XXZ Chain
• Thouless Energy Challenges Thermalization on the Ergodic Side of the Many-Body Localization Transition
• Universality and Critical Exponents of the Fermion Sign Problem
• Mobility edge in long-range interacting many-body localized systems
• Localization challenges quantum chaos in the finite two-dimensional Anderson model
• A note on the quasiperiodic many-body localization transition in dimension $d>1$
• Detecting ergodic bubbles at the crossover to many-body localization using neural networks
• Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations
• Signatures of a critical point in the many-body localization transition
• Catching thermal avalanches in the disordered XXZ model
• Many-body delocalization from embedded thermal inclusion
• Fractal nature of high-order time crystal phases
• Entanglement dynamics in the three-dimensional Anderson model
• Scrambling and Many-Body Localization in the XXZ-Chain
• Restoring ergodicity in a strongly disordered interacting chain
• Scaling properties of a spatial one-particle density-matrix entropy in many-body localized systems
• Signatures of quantum chaos in low-energy mixtures of few fermions
• Probability transport on the Fock space of a disordered quantum spin chain
• Universality classes of thermalization for mesoscopic Floquet systems
• The Fock-space landscape of many-body localisation
• Many-Body Mobility Edge in Quantum Sun models
• Mobility edges through inverted quantum many-body scarring
• Slow dynamics of a mobile impurity interacting with an Anderson insulator
• Ultraslow Growth of Number Entropy in an l-bit Model of Many-Body Localization
• Slow diffusion and Thouless localization criterion in modulated spin chains
• Many-body localization in one dimensional optical lattice with speckle disorder
• Tower of quantum scars in a partially many-body localized system
• Stark localization near Aubry-André criticality
• Investigating Berezinskii-Kosterlitz-Thouless phase transitions in Kagome spin ice by quantifying Monte Carlo process: Distribution of Hamming distances
• Absence of localization in interacting spin chains with a discrete symmetry
• Ergodic inclusions in many body localized systems
• Breaking the chains: extreme value statistics and localization in random spin chains
• The half-filled extended Hubbard model on a square lattice: Phase boundaries from determinant quantum Monte Carlo simulations
• Many-Body Localization: Transitions in Spin Models
• Sensitivity of the spectral form factor to short-range level statistics
• Signatures of many-body localization of quasiparticles in a flat band superconductor
• Absence of localization in two-dimensional Clifford circuits
• Eigenstate properties of the disordered Bose-Hubbard chain
• Tower of two-dimensional scar states in a localized system
• Higher-order topological insulator in a modified Haldane-Hubbard model
• Local integrals of motion and the stability of many-body localisation in Wannier-Stark potentials
• Many-body localization crossover is sharper in quasiperiodic spin chains
• Thermalization propagation front and robustness against avalanches in localized systems
• Slow propagation of information on the random XXZ quantum spin chain
• Enhanced many-body localization in a kinetically constrained model
• Strongly disordered Anderson insulator chains with generic two-body interaction
• Disorder in interacting quasi-one-dimensional systems: flat and dispersive bands
• Many body localization transition with correlated disorder
• Phenomenology of many-body localization in bond-disordered spin chains
• Quantum Chaos in Random Ising Networks
• What can we learn from diffusion about Anderson localization of a degenerate Fermi gas?
• Charge excitations across a superconductor-insulator transition
• Measuring out quasi-local integrals of motion from entanglement
• Finite-size prethermalization at the chaos-to-integrable crossover
• Cat states carrying long-range correlations in the many-body localized phase
• Semiclassical bounds on dynamics of two-dimensional interacting disordered fermions
• Many-body localization regime for cavity induced long-range interacting models
• Local integrals of motion in dipole-conserving models with Hilbert space fragmentation
• Superconducting Quantum Simulation for Many-Body Physics beyond Equilibrium
• Single-particle excitations across the localization and many-body localization transition in quasi-periodic systems
• Probing Hilbert space fragmentation and the block inverse participation ratio
• Supervised and unsupervised learning of the many-body critical phase, phase transitions, and critical exponents in disordered quantum systems
• Probing phase transitions with correlations in configuration space
• Quantum logarithmic multifractality
• Weyl semimetallic, Néel, spiral, and vortex states in the Rashba-Hubbard model
• Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder
• Long-ranged spectral correlations in eigenstate phases
• Modelling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains
• The role of interaction-induced tunneling in the dynamics of polar lattice bosons
• Operator Growth in Disordered Spin Chains: Indications for the Absence of Many-Body Localization
• The extended Hubbard model on a honeycomb lattice
• Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space
• Universal properties of single particle excitations across the many-body localization transition
• Measurement-induced phase transition in periodically driven free-fermionic systems
• Scaling theory of fading ergodicity
• Slow melting of a disordered quantum crystal
• Characterizing dynamical criticality of many-body localization transitions from the Fock-space perspective
• From Dyson Models to Many-Body Quantum Chaos
• Inhomogeneous Floquet thermalization
• Many-body localization in the infinite-interaction limit and the discontinuous eigenstate phase transition
• Nonergodic dynamics for an impurity interacting with bosons in tilted lattice
• Thermal avalanches in isolated many-body localized systems
• Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath
• Spin and energy diffusion vs. subdiffusion in disordered spin chains
• Ergodicity breaking transition in zero dimensions
• Low-Temperature Transport Property of Spin-1/2 Random Heisenberg Chains
• Delocalization in a partially disordered interacting many-body system
• Geometric quenches in quasi-disordered lattice system
• DisQu: Investigating the Impact of Disorder in Quantum Generative Models
• On the criticality of the configuration-space statistical geometry
• Long-range resonances in quasiperiodic many-body localization
• Phase Transitions and Critical Behavior in Quasi-One-Dimensional Two-Channel Systems with Quasiperiodic Disorder
• Spectral properties of three-dimensional Anderson model
• Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath
• Finite-size scalings in measurement-induced dynamical phase transition
• Localization transitions in quadratic systems without quantum chaos
• Universal Relation between Spectral and Wavefunction Properties at Criticality
• Many-body localization in a tilted potential in two dimensions
• Relaxation mechanisms in a disordered system with the Poisson level statistics
• Information Bounds on phase transitions in disordered systems
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain
• Phase Structure and Machine Learning Identification in One Dimensional Systems with Power Law Correlated Disorder and Long Range Hopping
• Spin-orbit coupled periodic Anderson model: Kondo-Dirac semimetal and orbital-selective antiferromagnetic semimetal
• Stability of the symmetry-protected topological phase and Ising transitions in a disordered U(1) quantum link model on a ladder
• Operator delocalization in disordered spin chains via exact MPO marginals
• Limitations of SVD-Based Diagnostics for Non-Hermitian Many-Body Localization with Time-Reversal Symmetry
• Localization with non-Hermitian off-diagonal disorder
• Critical Dynamics of the Anderson Transition on Small-World Graphs
• Many-body localization and particle multioccupancy in the disordered Bose-Hubbard model