Sub-ballistic growth of Rényi entropies due to diffusion

Abstract

We investigate the dynamics of quantum entanglement after a global quench and uncover a qualitative difference between the behavior of the von Neumann entropy and higher Rényi entropies. We argue that the latter generically grow \emph{sub-ballistically}, as $\propto \sqrt{t}$, in systems with diffusive transport. We provide strong evidence for this in both a U$(1)$ symmetric random circuit model and in a paradigmatic non-integrable spin chain, where energy is the sole conserved quantity. We interpret our results as a consequence of local quantum fluctuations in conserved densities, whose behavior is controlled by diffusion, and use the random circuit model to derive an effective description. We also discuss the late-time behavior of the second Rényi entropy and show that it exhibits hydrodynamic tails with \emph{three distinct power laws} occurring for different classes of initial states.

arXiv commentclose to published version: 4 + epsilon pages, 3 figures + supplement

References in corpus (41)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Efficient classical simulation of slightly entangled quantum computations
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• 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
• Quantum thermalization through entanglement in an isolated many-body system
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Operator Spreading in Random Unitary Circuits
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Holographic duality from random tensor networks
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Extended slow dynamical regime close to the many-body localization transition
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system
• Emergent statistical mechanics of entanglement in random unitary circuits
• Entanglement dynamics after quantum quenches in generic integrable systems
• Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• On entanglement spreading in chaotic systems
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• Dynamics of entanglement and transport in 1D systems with quenched randomness
• Hydrodynamic long-time tails after a quantum quench
• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Entanglement dynamics in quantum many-body systems
• Membrane theory of entanglement dynamics from holography
• Rényi entropies after releasing the Néel state in the XXZ spin-chain
• On entanglement spreading from holography
• Thermalization of entanglement
• Rényi entropies of generic thermodynamic macrostates in integrable systems
• Dynamics of Rényi entanglement entropy in diffusive qudit systems
• Dynamics of Renyi entanglement entropy in local quantum circuits with charge conservation

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• Random Quantum Circuits
• Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
• Entanglement phase transitions in measurement-only dynamics
• Measurement-induced phase transition: A case study in the non-integrable model by density-matrix renormalization group calculations
• Unitary circuits of finite depth and infinite width from quantum channels
• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
• The entanglement membrane in chaotic many-body systems
• Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
• Emergent conformal symmetry in non-unitary random dynamics of free fermions
• Many-Body Localization in the Age of Classical Computing
• Growth of entanglement entropy under local projective measurements
• Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
• Scrambling in Random Unitary Circuits: Exact Results
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Maximum velocity quantum circuits
• Entanglement spreading in non-equilibrium integrable systems
• Dynamics and Transport at the Threshold of Many-Body Localization
• Entanglement dynamics in hybrid quantum circuits
• Finite-size scaling of out-of-time-ordered correlators at late times
• Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
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• Heavy Operators and Hydrodynamic Tails
• Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
• Entanglement growth in diffusive systems
• Entanglement revivals as a probe of scrambling in finite quantum systems
• Hydrodynamics in lattice models with continuous non-Abelian symmetries
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• Operator backflow and the classical simulation of quantum transport
• Transport and entanglement growth in long-range random Clifford circuits
• Non-unitary dynamics of Sachdev-Ye-Kitaev chain
• Near-optimal covariant quantum error-correcting codes from random unitaries with symmetries
• Non-equilibrium dynamics of charged dual-unitary circuits
• Monitored fermions with conserved $\mathrm{U}(1)$ charge
• Diffusive scaling of Rényi entanglement entropy
• Entanglement growth after inhomogenous quenches
• Topological lower bound on quantum chaos by entanglement growth
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• Exact quench dynamics of the Floquet quantum East model at the deterministic point
• Emergent tracer dynamics in constrained quantum systems
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• Quantum information spreading in generalised dual-unitary circuits
• Calculating Renyi Entropies with Neural Autoregressive Quantum States
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• Signatures of information scrambling in the dynamics of the entanglement spectrum
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• From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Dynamics of Rényi entanglement entropy in diffusive qudit systems
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• Entanglement Diagnostics for Efficient Quantum Computation
• Fluctuations of subsystem entropies at late times
• Exact Entanglement in the Driven Quantum Symmetric Simple Exclusion Process
• Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
• Entanglement front generated by an impurity travelling in an isolated many-body quantum system
• Coarse-grained Entanglement and Operator Growth in Anomalous Dynamics
• Generalized Free Cumulants for Quantum Chaotic Systems
• Nonstabilizerness dynamics in many-body localized systems
• Subsystem Information Capacity in Random Circuits and Hamiltonian Dynamics
• Slow thermalization and subdiffusion in $U(1)$ conserving Floquet random circuits
• Entanglement dynamics in U(1) symmetric hybrid quantum automaton circuits
• The dynamical $\alpha$-Rényi entropies of local Hamiltonians grow at most linearly in time
• 1+1D Hadrons Minimize their Biparton Renyi Free Energy
• Two-dimensional local Hamiltonian problem with area laws is QMA-complete
• Semiclassical Limit of Measurement-Induced Transition in Many-Body Chaos in Integrable and Nonintegrable Oscillator Chains
• Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement
• Effective field theory of random quantum circuits
• Tuning the entanglement growth in matrix-product-state evolution of quantum systems by nonunitary similarity transformations
• Energy-filtered quantum states and the emergence of non-local correlations
• Entanglement of Disjoint Intervals in Dual-Unitary Circuits: Exact Results
• Measurement-induced phase transitions in systems with diffusive dynamics
• Structural Stability Hypothesis of Dual Unitary Quantum Chaos
• Persistent Ballistic Entanglement Spreading with Optimal Control in Quantum Spin Chains
• Efficient post-selection in light-cone correlations of monitored quantum circuits
• More on the Operator Space Entanglement (OSE): Rényi OSE, revivals, and integrability breaking
• Logarithmic light cone, slow entanglement growth, and quantum memory
• Exact quench dynamics of symmetry resolved entanglement in a free fermion chain
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• Entanglement dynamics of multi-parametric random states: a single parametric formulation
• Subexponential decay of local correlations from diffusion-limited dephasing
• Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture
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