Hydrodynamic Diffusion in Integrable Systems

Abstract

We show that hydrodynamic diffusion is generically present in many-body interacting integrable models. We extend the recently developed generalised hydrodynamic (GHD) to include terms of Navier-Stokes type which lead to positive entropy production and diffusive relaxation mechanisms. These terms provide the subleading diffusive corrections to Euler-scale GHD for the large-scale non-equilibrium dynamics of integrable systems, and arise due to two-body scatterings among quasiparticles. We give exact expressions for the diffusion coefficients. Our results apply to a large class of integrable models, including quantum and classical, Galilean and relativistic field theories, chains and gases in one dimension, such as the Lieb-Liniger model describing cold atom gases and the Heisenberg quantum spin chain. We provide numerical evaluations in the Heisenberg spin chain, both for the spin diffusion constant, and for the diffusive effects during the melting of a small domain wall of spins, finding excellent agreement with tDMRG numerical simulations.

5 pages + SM, 1 figure. Definition of \mathfrak{D} added

References in corpus (86)

• Quantum many-body systems out of equilibrium
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Generalized Gibbs ensemble in integrable lattice models
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Time evolution of local observables after quenching to an integrable model
• Transport and conservation laws
• Viscosity Bound and Causality Violation
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Spin and Charge Resolved Quantum Gas Microscopy of Antiferromagnetic Order in Hubbard Chains
• Fluctuations in Stationary non Equilibrium States
• Spin diffusion from an inhomogeneous quench in an integrable system
• Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
• Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain
• Soliton gases and generalized hydrodynamics
• "Light-cone" dynamics after quantum quenches in spin chains
• Diffusion and ballistic transport in one-dimensional quantum systems
• Solvable Hydrodynamics of Quantum Integrable Systems
• Thermalization near integrability in a dipolar quantum Newton's cradle
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• 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
• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Analytic solution of the Domain Wall non-equilibrium stationary state
• Energy flow in non-equilibrium conformal field theory
• Heat transport in low dimensions: introduction and phenomenology
• Generalized global symmetries and dissipative magnetohydrodynamics
• A note on generalized hydrodynamics: inhomogeneous fields and other concepts
• Dynamics of hard rods with initial domain wall state
• A geometric viewpoint on generalized hydrodynamics
• Drude Weight for the Lieb-Liniger Bose Gas
• Form factors in finite volume I: form factor bootstrap and truncated conformal space
• Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains
• Real-time and real-space spin- and energy dynamics in one-dimensional spin-1/2 systems induced by local quantum quenches at finite temperatures
• Hydrodynamic theory of thermoelectric transport and negative magnetoresistance in Weyl semimetals
• Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
• Recurrences in an isolated quantum many-body system
• Entanglement evolution and generalised hydrodynamics: noninteracting systems
• From Interacting Particles to Equilibrium Statistical Ensembles
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• Entanglement and quantum transport in integrable systems
• The thermodynamic limit of the Whitham equations
• Non-equilibrium steady states in the Klein-Gordon theory
• Dephasing-induced diffusive transport in anisotropic Heisenberg model
• Finite-temperature lineshapes in gapped quantum spin chains
• Quantum quench from a thermal tensor state: boundary effects and generalized Gibbs ensemble
• String-charge duality in integrable lattice models
• Inhomogeneous Quantum Quenches
• Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
• Diffusion in deterministic interacting lattice systems
• Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics
• Stationary states in a free fermionic chain from the Quench Action Method
• Time-dependent generalized Gibbs ensembles in open quantum systems
• Energy transport in Heisenberg chains beyond the Luttinger liquid paradigm
• Thermodyamic bounds on Drude weights in terms of almost-conserved quantities
• Incomplete thermalization from trap-induced integrability breaking: lessons from classical hard rods
• Ballistic front dynamics after joining two semi-infinite quantum Ising chains
• Lower Bounding Diffusion Constant by the Curvature of Drude Weight
• Finite-temperature form factors in the free Majorana theory
• Pumping approximately integrable systems
• The Quantum Double in Integrable Quantum Field Theory
• Universal front propagation in the quantum Ising chain with domain-wall initial states
• Emergent eigenstate solution to quantum dynamics far from equilibrium
• Energy transport in an integrable parafermionic chain via generalized hydrodynamics
• Universal broadening of the light cone in low-temperature transport
• Non-Equilibrium Mass Transport in the 1D Fermi-Hubbard Model
• Current fluctuations for anharmonic chains in thermal equilibrium
• Transport properties of the one-dimensional Hubbard model at finite temperature
• Interacting and noninteracting integrable systems
• The Dynamic Structure Factor of the 1D Bose Gas near the Tonks-Girardeau Limit
• On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems
• Low-Temperature Transport in Out-of-Equilibrium XXZ Chains
• Particle-hole pairs and density-density correlations in the Lieb-Liniger model
• Finite-Temperature Form Factors: a Review
• Edge singularities and quasi-long-range order in non-equilibrium steady states
• Monitoring squeezed collective modes of a one-dimensional Bose gas after an interaction quench using density ripples analysis
• Spinon and bound state excitation "light cones" in Heisenberg XXZ Chains
• Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures
• Real-Time Dynamics of Typical and Untypical States in Non-Integrable Systems
• Anomalous and regular transport in spin 1/2 chains: AC conductivity
• Charge diffusion in the one-dimensional Hubbard model

Cited by in corpus (199)

• Finite-temperature transport in one-dimensional quantum lattice models
• A Universal Operator Growth Hypothesis
• Generalized HydroDynamics on an Atom Chip
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Lecture notes on Generalised Hydrodynamics
• Generalized hydrodynamics in strongly interacting 1D Bose gases
• Quantum Generalized Hydrodynamics
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Generalized hydrodynamics with space-time inhomogeneous interactions
• Superdiffusion in spin chains
• Diffusive hydrodynamics from integrability breaking
• Correlation functions and transport coefficients in generalised hydrodynamics
• Holography and hydrodynamics with weakly broken symmetries
• Anomalous spin diffusion in one-dimensional antiferromagnets
• Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Extension of the Generalized Hydrodynamics to the Dimensional Crossover Regime
• Superuniversality of superdiffusion
• Generalised hydrodynamics of the classical Toda system
• Non-Equilibrium Dynamics and Weakly Broken Integrability
• Hydrodynamics of weak integrability breaking
• Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
• Superdiffusion from emergent classical solitons in quantum spin chains
• Entanglement evolution and generalised hydrodynamics: interacting integrable systems
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Breakdown of hydrodynamics below four dimensions in a fracton fluid
• Kardar-Parisi-Zhang universality from soft gauge modes
• Emergent hydrodynamics in a strongly interacting dipolar spin ensemble
• Thermalisation of a trapped one-dimensional Bose gas via diffusion
• Open Quantum Symmetric Simple Exclusion Process
• Stability of superdiffusion in nearly integrable spin chains
• Kardar-Parisi-Zhang Scaling for an Integrable Lattice Landau-Lifshitz Spin Chain
• Fluctuations in ballistic transport from Euler hydrodynamics
• Algebraic construction of current operators in integrable spin chains
• Transport fluctuations in integrable models out of equilibrium
• Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics
• Generalised hydrodynamics with dephasing noise
• Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice
• Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
• Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence
• Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport
• Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
• Integrable many-body quantum Floquet-Thouless pumps
• Universality classes of spin transport in one-dimensional isotropic magnets: the onset of logarithmic anomalies
• Spin crossovers and superdiffusion in the one-dimensional Hubbard model
• Domain-wall melting in the spin-$1/2$ XXZ spin chain: emergent Luttinger liquid with fractal quasi-particle charge
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Ballistic macroscopic fluctuation theory
• The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges
• Integrability-protected adiabatic reversibility in quantum spin chains
• Locally quasi-stationary states in noninteracting spin chains
• Equations of state in generalized hydrodynamics
• From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
• Absence of Normal Fluctuations in an Integrable Magnet
• Generalized hydrodynamics of the KdV soliton gas
• The spin Drude weight of the XXZ chain and generalized hydrodynamics
• Emergence of hydrodynamic spatial long-range correlations in nonequilibrium many-body systems
• Generalized hydrodynamics regime from the thermodynamic bootstrap program
• Exact description of quantum stochastic models as quantum resistors
• Collision rate ansatz for quantum integrable systems
• Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point
• Generalized hydrodynamics: a perspective
• Anomalous low-frequency conductivity in easy-plane XXZ spin chains
• Form factors and generalized hydrodynamics for integrable systems
• Subdiffusive front scaling in interacting integrable models
• Anomalous transport from hot quasiparticles in interacting spin chains
• Diffusive Heat Waves in Random Conformal Field Theory
• Emergent Pauli blocking in a weakly interacting Bose gas
• Diffusion and operator entanglement spreading
• Time-dependent matrix product ansatz for interacting reversible dynamics
• Hydrodynamics of nonintegrable systems from a relaxation-time approximation
• Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems
• Asymmetry in energy versus spin transport in certain interacting, disordered systems
• Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models
• High-temperature spin dynamics in the Heisenberg chain: Magnon propagation and emerging KPZ-scaling in the zero-magnetization limit
• Integrable Matrix Models in Discrete Space-Time
• Distinct universality classes of diffusive transport from full counting statistics
• Generalized Hydrodynamic approach to charge and energy currents in the one-dimensional Hubbard model
• Magnetization and entanglement after a geometric quench in the XXZ chain
• Dynamics of Fluctuations in Quantum Simple Exclusion Processes
• Thermodynamic bootstrap program for integrable QFT's: Form factors and correlation functions at finite energy density
• The one-dimensional Bose gas with strong two-body losses: the effect of the harmonic confinement
• Free fermions at the edge of interacting systems
• Universal anomalous fluctuations in charged single-file systems
• Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation
• $T\bar{T}$-deformed conformal field theories out of equilibrium
• Superdiffusive transport of energy in one-dimensional metals
• Exact Thermodynamics and Transport in the Classical Sine-Gordon Model
• Generalized hydrodynamics study of the one-dimensional Hubbard model: Stationary clogging and proportionality of spin, charge, and energy currents
• Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains
• One-dimensional Quantum Spin Dynamics of Bethe String States
• Dynamics of large deviations in the hydrodynamic limit: Non-interacting systems
• Generalized hydrodynamics in box-ball system
• Diffusion and superdiffusion from hydrodynamic projections
• Ballistic transport and boundary resistances in inhomogeneous quantum spin chains
• Euler-scale dynamical correlations in integrable systems with fluid motion
• Diffusive Hydrodynamics of Inhomogenous Hamiltonians
• Microscopic theory of the fluctuating hydrodynamics in nonlinear lattices
• Thermal transport in $T\bar{T}$-deformed conformal field theories: from integrability to holography
• Diffusion from Convection
• Real-time scattering of interacting quasiparticles in quantum spin chains
• Adiabatic formation of bound states in the 1d Bose gas
• Exploiting disorder to probe spin and energy hydrodynamics
• Magnetization and energy dynamics in spin ladders: Evidence of diffusion in time, frequency, position, and momentum
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Can the Macroscopic Fluctuation Theory be Quantized?
• Entropy growth during free expansion of an ideal gas
• Operator front broadening in chaotic and integrable quantum chains
• Transport through interacting defects and lack of thermalisation
• Magnetization dynamics in clean and disordered spin-1 XXZ chains
• Emergent entropy production and hydrodynamics in quantum many-body systems
• Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
• Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet
• Linearized regime of the generalized hydrodynamics with diffusion
• How generalized hydrodynamics time evolution arises from a form factor expansion
• Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Hydrodynamic Equations for the Toda Lattice
• Non-Gaussian diffusive fluctuations in Dirac fluids
• Interplay between transport and quantum coherences in free fermionic systems
• Quantum Hydrodynamics in Spin Chains with Phase Space Methods
• The dissipative Generalized Hydrodynamic equations and their numerical solution
• Ballistic-to-diffusive transition in spin chains with broken integrability
• Integrability breaking in the one dimensional Bose gas: Atomic losses and energy loss
• Scaling of fronts and entanglement spreading during a domain wall melting
• Diffusive hydrodynamics from long-range correlations
• Exact large-scale fluctuations of the phase field in the sine-Gordon model
• Coexistence of diffusive and ballistic transport in integrable quantum lattice models
• Emergent ballistic transport of Bose-Fermi mixtures in one dimension
• From dissipationless to normal diffusion in easy-axis Heisenberg spin chain
• Dynamics of fluctuation correlation in periodically driven classical system
• Corrections to diffusion in interacting quantum systems
• Anisotropic Landau-Lifshitz Model in Discrete Space-Time
• Long-lived Solitons and Their Signatures in the Classical Heisenberg Chain
• Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem
• Transport and entanglement across integrable impurities from Generalized Hydrodynamics
• Popcorn Drude weights from quantum symmetry
• Integrability breaking in the Rule 54 cellular automaton
• The Fredkin staircase: An integrable system with a finite-frequency Drude peak
• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• Integrability breaking from backscattering
• Multiple relaxation times in perturbed XXZ chain
• Hydrodynamic relaxation of spin helices
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Navier-Stokes equations for nearly integrable quantum gases
• On the Hydrodynamics of Unstable Excitations
• Analytical results for the low-temperature Drude weight of the XXZ spin chain
• Benchmarks of Generalized Hydrodynamics for 1D Bose Gases
• Finite temperature spin diffusion in the Hubbard model in the strong coupling limit
• Characterising transport in a quantum gas by measuring Drude weights
• Anomalous current fluctuations from Euler hydrodynamics
• Coherent spin-phonon scattering in facilitated Rydberg lattices
• Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case
• Exact time evolution formulae in the XXZ spin chain with domain wall initial state
• Evidences for interaction-induced Haldane fractional exclusion statistics in one and higher dimensions
• Undular diffusion in nonlinear sigma models
• High-low pressure domain wall for the classical Toda lattice
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• The Staircase Model: Massless Flows and Hydrodynamics
• Soliton gas of the integrable Boussinesq equation and its generalised hydrodynamics
• Thermalization and hydrodynamics in an interacting integrable system: the case of hard rods
• The propagator of the finite XXZ spin-$\frac{1}{2}$ chain
• Diffusive charge transport in the gapped 1D Hubbard model at all finite temperatures
• Connected correlations in partitioning protocols: a case study and beyond
• The relevant excitations for the one-body function in the Lieb-Liniger model
• Identifying diffusive length scales in one-dimensional Bose gases
• The Theory of Generalised Hydrodynamics for the One-dimensional Bose Gas
• Hydrodynamics of a hard-core active lattice gas
• Emergent Infrared Conformal Dynamics in Strongly Interacting Quantum Gases
• Experimental Investigation of a Bipartite Quench in a 1D Bose gas
• Non-linear Transport by Bethe Bound States
• Generalized hydrodynamics in complete box-ball system for $U_q({\widehat{sl}}_n)$
• Finding local integrals of motion in quantum lattice models in the thermodynamic limit
• Simulating generalised fluids via interacting wave packets evolution
• Integrable hydrodynamics of Toda chain: case of small systems
• Emergence of generalized hydrodynamics in the non-local Luttinger model
• Thouless approach in transport in integrable and perturbed easy-axis Heisenberg chains
• Anomalous charge transport in the sine-Gordon model
• Non-Equilibrium Steady State of the Lieb-Liniger model: exact treatment of the Tonks Girardeau limit
• Thermalization/Relaxation in integrable and free field theories: an Operator Thermalization Hypothesis
• A hydrodynamic approach to Stark localization
• Diagnosing quantum transport from wave function snapshots
• Separation of variables for higher rank integrable models: review of recent progress
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model
• Superdiffusion resilience in Heisenberg Chains with 2D interactions on a quantum processor
• Hydrodynamics of spin transport in the Haldane-Shastry chain
• Tunable superdiffusion in integrable spin chains using correlated initial states
• Dynamic structure factor of quantum hard rods from exact form-factors
• Exact Spectral Function of One-Dimensional Bose Gases
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