Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains

Abstract

We study the nonequilibrium dynamics of random spin chains that remain integrable (i.e., solvable via Bethe ansatz): because of correlations in the disorder, these systems escape localization and feature ballistically spreading quasiparticles. We derive a generalized hydrodynamic theory for dynamics in such random integrable systems, including diffusive corrections due to disorder, and use it to study non-equilibrium energy and spin transport. We show that diffusive corrections to the ballistic propagation of quasiparticles can arise even in noninteracting settings, in sharp contrast with clean integrable systems. This implies that operator fronts broaden diffusively in random integrable systems. By tuning parameters in the disorder distribution, one can drive this model through an unusual phase transition, between a phase where all wavefunctions are delocalized and a phase in which low-energy wavefunctions are quasi-localized (in a sense we specify). Both phases have ballistic transport; however, in the quasi-localized phase, local autocorrelation functions decay with an anomalous power law, and the density of states diverges at low energy.

14 pages, 10 figures

References in corpus (69)

• Many-Body Physics with Ultracold Gases
• The nitrogen-vacancy colour centre in diamond
• Many body localization and thermalization in quantum statistical mechanics
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• A bound on chaos
• Anderson Transitions
• 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
• Time-dependence of correlation functions following a quantum quench
• State preservation by repetitive error detection in a superconducting quantum circuit
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Operator Spreading in Random Unitary Circuits
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Experimental Observation of a Generalized Gibbs Ensemble
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Time evolution of local observables after quenching to an integrable model
• Breakdown of thermalization in finite one-dimensional systems
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• 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
• Entanglement Tsunami: Universal Scaling in Holographic Thermalization
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Many-body localization in one dimension as a dynamical renormalization group fixed point
• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• Hydrodynamic Diffusion in Integrable Systems
• Quasilocal charges in integrable lattice systems
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Solution of a minimal model for many-body quantum chaos
• Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain
• Soliton gases and generalized hydrodynamics
• Constructing the generalized Gibbs ensemble after a quantum quench
• "Light-cone" dynamics after quantum quenches in spin chains
• Families of quasi-local conservation laws and quantum spin transport
• Solvable Hydrodynamics of Quantum Integrable Systems
• Thermalization near integrability in a dipolar quantum Newton's cradle
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
• Large-scale description of interacting one-dimensional Bose gases: generalized hydrodynamics supersedes conventional hydrodynamics
• Microscopic origin of ideal conductivity in integrable quantum models
• Conformal field theory out of equilibrium: a review
• Kinetic equation for a dense soliton gas
• Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• On entanglement spreading in chaotic systems
• Analytic solution of the Domain Wall non-equilibrium stationary state
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Out-of-time-ordered correlators in quantum Ising chain
• A note on generalized hydrodynamics: inhomogeneous fields and other concepts
• Drude Weight for the Lieb-Liniger Bose Gas
• Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
• Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
• Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
• Spread of entanglement and causality
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• The thermodynamic limit of the Whitham equations
• Exact large-scale correlations in integrable systems out of equilibrium
• Incomplete thermalization from trap-induced integrability breaking: lessons from classical hard rods
• Particle-hole symmetry, many-body localization, and topological edge modes
• Thermodynamics of Integrable Chains with Alternating Spins
• Interacting and noninteracting integrable systems
• Subdiffusive front scaling in interacting integrable models
• Diffusive Heat Waves in Random Conformal Field Theory
• Integrable spin chains with random interactions
• Temporal Diffusion

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• From compact localized states to many-body scars in the random quantum comb
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