Entanglement revivals as a probe of scrambling in finite quantum systems

Abstract

The entanglement evolution after a quantum quench became one of the tools to distinguish integrable versus chaotic (non-integrable) quantum many-body dynamics. Following this line of thoughts, here we propose that the revivals in the entanglement entropy provide a finite-size diagnostic benchmark for the purpose. Indeed, integrable models display periodic revivals manifested in a dip in the block entanglement entropy in a finite system. On the other hand, in chaotic systems, initial correlations get dispersed in the global degrees of freedom (information scrambling) and such a dip is suppressed. We show that while for integrable systems the height of the dip of the entanglement of an interval of fixed length decays as a power law with the total system size, upon breaking integrability a much faster decay is observed, signalling strong scrambling. Our results are checked by exact numerical techniques in free-fermion and free-boson theories, and by time-dependent density matrix renormalisation group in interacting integrable and chaotic models.

arXiv comment19 pages, 7 figures. Added two figures and one appendix. As published

References in corpus (161)

• The density-matrix renormalization group in the age of matrix product states
• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• A bound on chaos
• 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
• Black holes and the butterfly effect
• Real time evolution using the density matrix renormalization group
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Time-dependence of correlation functions following a quantum quench
• Measuring entanglement entropy through the interference of quantum many-body twins
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Quantum thermalization through entanglement in an isolated many-body system
• Calculation of reduced density matrices from correlation functions
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Quantum entanglement in condensed matter systems
• Reduced density matrices and entanglement entropy in free lattice models
• Operator Spreading in Random Unitary Circuits
• Chaos in quantum channels
• Quantum Quench in the Transverse Field Ising Chain
• Generalized Gibbs ensemble in integrable lattice models
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Experimental Observation of a Generalized Gibbs Ensemble
• Probing entanglement entropy via randomized measurements
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• Probing entanglement in a many-body-localized system
• The Luttinger model following a sudden interaction switch-on
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Dephasing and the steady state in quantum many-particle systems
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Real time confinement following a quantum quench to a non-integrable model
• Alternatives to Eigenstate Thermalization
• Reduced Density Matrix after a Quantum Quench
• Quench dynamics across quantum critical points
• Entanglement in a fermion chain under continuous monitoring
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Entanglement of Quantum Evolutions
• Solution of a minimal model for many-body quantum chaos
• Entanglement dynamics after quantum quenches in generic integrable systems
• Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
• "Light-cone" dynamics after quantum quenches in spin chains
• Prethermalization and thermalization in models with weak integrability breaking
• Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases
• Prethermalization and universal dynamics in near-integrable quantum systems
• Exact dynamics in dual-unitary quantum circuits
• Operator space entanglement entropy in transverse Ising chain
• Quantum Quenches in Integrable Field Theories
• What is an integrable quench?
• Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
• Complexity and entanglement for thermofield double states
• Scrambling and entanglement spreading in long-range spin chains
• Analytic solution of the Domain Wall non-equilibrium stationary state
• Full counting statistics in a propagating quantum front and random matrix spectra
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• Entanglement in solvable many-particle models
• A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states
• A quantum hydrodynamical description for scrambling and many-body chaos
• Entanglement Scrambling in 2d Conformal Field Theory
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Generalized Gibbs Ensembles for Quantum Field Theories
• Entanglement growth and correlation spreading with variable-range interactions in spin and fermionic tunnelling models
• Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Pre-thermalization in a non-integrable quantum spin chain after a quench
• Equilibration of a Tonks-Girardeau gas following a trap release
• Quench Dynamics in a Model with Tuneable Integrability Breaking
• Thermalization and Quantum Correlations in Exactly Solvable Models
• Sub-ballistic growth of Rényi entropies due to diffusion
• Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1+1d
• Is efficiency of classical simulations of quantum dynamics related to integrability?
• Entanglement and matrix elements of observables in interacting integrable systems
• Thermalization and Revivals after a Quantum Quench in Conformal Field Theory
• Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains
• Inhomogeneous field theory inside the arctic circle
• Generalized hydrodynamics with space-time inhomogeneous interactions
• Quantum Quench from a Thermal Initial State
• Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
• Entanglement entropy of two disjoint blocks in critical Ising models
• Generalized TBA and generalized Gibbs
• Local quantum quenches in critical one-dimensional systems: entanglement, the Loschmidt echo, and light-cone effects
• Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
• Entanglement evolution and generalised hydrodynamics: noninteracting systems
• Dynamics of entanglement and transport in 1D systems with quenched randomness
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Quantum revivals and many-body localization
• Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases
• Operator Space Entanglement Entropy in XY Spin Chains
• Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap
• Mutual information after a local quench in conformal field theory
• Entanglement and quantum transport in integrable systems
• Quench action and Renyi entropies in integrable systems
• Inhomogeneous quenches in a fermionic chain: exact results
• Unitary $n$-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Thermalization of mutual and tripartite information in strongly coupled two dimensional conformal field theories
• Entanglement Growth after a Global Quench in Free Scalar Field Theory
• Slow quantum thermalization and many-body revivals from mixed phase space
• Entanglement evolution and generalised hydrodynamics: interacting integrable systems
• Entanglement dynamics in short and long-range harmonic oscillators
• Entanglement spreading after a geometric quench in quantum spin chains
• Multi-speed prethermalization in spin models with power-law decaying interactions
• Density Matrices for a Chain of Oscillators
• Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
• Random matrices and entanglement entropy of trapped Fermi gases
• Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories
• Entanglement in a periodic quench
• Quantum information dynamics in multipartite integrable systems
• On Generalized Gibbs Ensembles with an infinite set of conserved charges
• Quantum quenches from excited states in the Ising chain
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate
• Quantum information scrambling after a quantum quench
• Complexity of thermal states in quantum spin chains
• Correlations and diagonal entropy after quantum quenches in XXZ chains
• Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits
• Finite-size corrections vs. relaxation after a sudden quench
• Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
• Entanglement production in bosonic systems: Linear and logarithmic growth
• Rényi entropies after releasing the Néel state in the XXZ spin-chain
• Memory-preserving equilibration after a quantum quench in a 1d critical model
• Exact solution for the quench dynamics of a nested integrable system
• Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
• Entanglement growth in diffusive systems
• Entanglement Tsunami in (1+1)-Dimensions
• Entanglement hamiltonians in 1D free lattice models after a global quantum quench
• Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
• Spreading of entanglement and correlations after a quench with intertwined quasiparticles
• Multicritical edge statistics for the momenta of fermions in non-harmonic traps
• Quantum vs. classical information: operator negativity as a probe of scrambling
• Growth of mutual information in a quenched one-dimensional open quantum many body system
• Stationary entropies after a quench from excited states in the Ising chain
• Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
• The quench action approach in finite integrable spin chains
• Rényi entropies of generic thermodynamic macrostates in integrable systems
• Entanglement Evolution in Lifshitz-type Scalar Theories
• Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
• Quasilocal charges and progress towards the complete GGE for field theories with non-diagonal scattering
• Magnetization and entanglement after a geometric quench in the XXZ chain
• Quasi-local charges and the Generalized Gibbs Ensemble in the Lieb-Liniger model
• Light-cone velocities after a global quench in a non-interacting model
• Dynamical manifestation of Gibbs paradox after a quantum quench
• Measuring effective temperatures in a generalized Gibbs ensemble
• Free fermions at the edge of interacting systems
• Prethermalization at Low Temperature: the Scent of Long-Range Order
• Prethermalization from a low-density Holstein-Primakoff expansion
• Searching for the Tracy-Widom distribution in nonequilibrium processes
• Entanglement growth after inhomogenous quenches
• Diffusive scaling of Rényi entanglement entropy
• On the possibility of complete revivals after quantum quenches to a critical point
• Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach
• Entanglement spreading and quasiparticle picture beyond the pair structure
• Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics
• Return amplitude after a quantum quench in the XY chain
• Correlation and entanglement spreading in nested spin chains

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• Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions
• Coherent and dissipative dynamics at quantum phase transitions
• Entanglement spreading in non-equilibrium integrable systems
• Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
• Hydrodynamics of quantum entropies in Ising chains with linear dissipation
• Many-body dynamical phase transition in quasi-periodic potential
• Quenching from superfluid to free bosons in two dimensions: entanglement, symmetries, and quantum Mpemba effect
• Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system
• Entanglement dynamics in the many-body Hatano-Nelson model
• Prethermalisation and Thermalisation in the Entanglement Dynamics
• Entanglement transitions as a probe of quasiparticles and quantum thermalization
• Quantum critical systems with dissipative boundaries
• Dynamics after quenches in one-dimensional quantum Ising-like systems
• Entanglement evolution after a global quench across a conformal defect
• Witnessing quantum chaos using observational entropy
• Quantum information scrambling in non-Markovian open quantum systems
• Negative tripartite mutual information after quantum quenches in integrable systems
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Entanglement dynamics of thermofield double states in integrable models
• Experimentally probing Landauer's principle in the quantum many-body regime
• Subsystem Information Capacity in Random Circuits and Hamiltonian Dynamics
• Subsystem complexity after a local quantum quench
• Information Trapping by Topologically Protected Edge States: Scrambling and the Butterfly Velocity
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Mesoscopic fluctuations in entanglement dynamics
• Out-of-equilibrium dynamics across the first-order quantum transitions of one-dimensional quantum Ising models
• Quench dynamics of Rényi negativities and the quasiparticle picture
• Entanglement in dual unitary quantum circuits with impurities
• Aspects of entanglement in non-local field theories with fractional Laplacian
• Exact quench dynamics of symmetry resolved entanglement in a free fermion chain
• Measurement-induced phase transition in periodically driven free-fermionic systems
• More on the Operator Space Entanglement (OSE): Rényi OSE, revivals, and integrability breaking
• Relaxation of antiferromagnetic order and growth of Rényi entropy in a generalized Heisenberg star
• Scrambling in Ising spin systems with periodic transverse magnetic fields
• Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture
• Configurable photonic simulator for quantum field dynamics
• Dynamics of charge-imbalance-resolved entanglement negativity after a quench in a free-fermion model
• Odd Entanglement Entropy and Logarithmic Negativity for Thermofield Double States
• Symmetry resolved out-of-time-order correlators of Heisenberg spin chains using projected matrix product operators
• The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes
• Volume-law entanglement entropy of typical pure quantum states