Diffusion in generalized hydrodynamics and quasiparticle scattering

Abstract

We extend beyond the Euler scales the hydrodynamic theory for quantum and classical integrable models developed in recent years, accounting for diffusive dynamics and local entropy production. We review how the diffusive scale can be reached via a gradient expansion of the expectation values of the conserved fields and how the coefficients of the expansion can be computed via integrated steady-state two-point correlation functions, emphasising that PT-symmetry can fully fix the inherent ambiguity in the definition of conserved fields at the diffusive scale. We develop a form factor expansion to compute such correlation functions and we show that, while the dynamics at the Euler scale is completely determined by the density of single quasiparticle excitations on top of the local steady state, diffusion is due to scattering processes among quasiparticles, which are only present in truly interacting systems. We then show that only two-quasiparticle scattering processes contribute to the diffusive dynamics. Finally we employ the theory to compute the exact spin diffusion constant of a gapped XXZ spin-1/2 chain at finite temperature and half-filling, where we show that spin transport is purely diffusive.

57 pages + bibliography. 4 figures

References in corpus (157)

• Thermalization and its mechanism for generic isolated quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Black holes and the butterfly effect
• Quantum many-body systems out of equilibrium
• Time-dependence of correlation functions following a quantum quench
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Operator Spreading in Random Unitary Circuits
• Generalized Gibbs ensemble in integrable lattice models
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• 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
• Transport and conservation laws
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Viscosity Bound and Causality Violation
• 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
• Spin and Charge Resolved Quantum Gas Microscopy of Antiferromagnetic Order in Hubbard Chains
• Susceptibility of the Spin 1/2 Heisenberg Antiferromagnetic Chain
• Generalized HydroDynamics on an Atom Chip
• Hydrodynamic Diffusion in Integrable Systems
• Spin diffusion from an inhomogeneous quench in an integrable system
• Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain
• Soliton gases and generalized hydrodynamics
• Entanglement dynamics after quantum quenches in generic integrable systems
• Families of quasi-local conservation laws and quantum spin transport
• Solvable Hydrodynamics of Quantum Integrable Systems
• Quantum quench dynamics
• Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases
• Thermalization near integrability in a dipolar quantum Newton's cradle
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• 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
• Quantum Quenches in Integrable Field Theories
• 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
• Super-diffusion in one-dimensional quantum lattice models
• Dynamics of Bose condensed gases in highly deformed traps
• Generalized global symmetries and dissipative magnetohydrodynamics
• Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures
• 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
• Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling
• Drude Weight for the Lieb-Liniger Bose Gas
• One-particle dynamical correlations in the one-dimensional Bose gas
• Form factors in finite volume I: form factor bootstrap and truncated conformal space
• Form factor approach to dynamical correlation functions in critical models
• Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
• 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
• Exact local correlations and full counting statistics for arbitrary states of the one-dimensional interacting Bose gas
• Entanglement evolution and generalised hydrodynamics: noninteracting systems
• Spin-current autocorrelations from single pure-state propagation
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• Determination of the Nonequilibrium Steady State Emerging from a Defect
• The thermodynamic limit of the Whitham equations
• Exact large-scale correlations in integrable systems out of equilibrium
• Non-equilibrium steady-states in conformal field theory
• 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
• Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model
• A comment on finite temperature correlations in integrable QFT
• Quantum quench from a thermal tensor state: boundary effects and generalized Gibbs ensemble
• String-charge duality in integrable lattice models
• Inhomogeneous Quantum Quenches
• Form factor expansion for thermal correlators
• Exactly conserved quasilocal operators for the XXZ spin chain
• Diffusion in deterministic interacting lattice systems
• Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
• Quantum thermalization dynamics with Matrix-Product States
• Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics
• Exact three-body local correlations for excited states of the 1D Bose gas
• Finite temperature correlations in the one-dimensional quantum Ising model
• 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
• Hybrid semiclassical theory of quantum quenches in one dimensional systems
• Universal relaxational dynamics of gapped one dimensional models in the quantum sine-Gordon universality class
• Finite-temperature Drude weight within the anisotropic Heisenberg chain
• Thermodyamic bounds on Drude weights in terms of almost-conserved quantities
• Mean values of local operators in highly excited Bethe states
• Incomplete thermalization from trap-induced integrability breaking: lessons from classical hard rods
• Ballistic front dynamics after joining two semi-infinite quantum Ising chains
• Low temperature correlation functions in integrable models: Derivation of the large distance and time asymptotics from the form factor expansion
• Lower Bounding Diffusion Constant by the Curvature of Drude Weight
• Finite-temperature form factors in the free Majorana theory
• Universal front propagation in the quantum Ising chain with domain-wall initial states
• Spin-charge separation effects in the low-temperature transport of 1D Fermi gases
• Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics
• Emergent eigenstate solution to quantum dynamics far from equilibrium
• Energy transport in an integrable parafermionic chain via generalized hydrodynamics
• Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps
• Short distance correlators in the XXZ spin chain for arbitrary string distributions
• Macroscopic Diffusive Transport in a Microscopically Integrable Hamiltonian System
• Excitation spectrum of the Lieb-Liniger model
• Universal broadening of the light cone in low-temperature transport
• Thermal form-factor approach to dynamical correlation functions of integrable lattice models
• Non-Equilibrium Mass Transport in the 1D Fermi-Hubbard Model
• Integrability-protected adiabatic reversibility in quantum spin chains
• Transport properties of the one-dimensional Hubbard model at finite temperature
• Finite-time universality in nonequilibrium CFT
• Equations of state in generalized hydrodynamics
• Interacting and noninteracting integrable systems
• The spin Drude weight of the XXZ chain and generalized hydrodynamics
• Time evolution of the Luttinger model with nonuniform temperature profile
• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• Collective oscillations of one-dimensional Bose-Einstein gas in a time-varying trap potential and atomic scattering length
• Finite temperature correlation functions from form factors
• The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases
• The Dynamic Structure Factor of the 1D Bose Gas near the Tonks-Girardeau Limit
• On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems
• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
• Finite-temperature hydrodynamics for one-dimensional Bose gases: Breathing mode oscillations as a case study
• Subdiffusive front scaling in interacting integrable models
• Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium
• Low-Temperature Transport in Out-of-Equilibrium XXZ Chains
• Excited state correlations of the finite Heisenberg chain
• Particle-hole pairs and density-density correlations in the Lieb-Liniger model
• Diffusive Heat Waves in Random Conformal Field Theory
• Finite-Temperature Form Factors: a Review
• Exactly solvable deterministic lattice model of crossover between ballistic and diffusive transport
• Edge singularities and quasi-long-range order in non-equilibrium steady states
• On the thermodynamic limit of form factor expansions of dynamical correlation functions in the massless regime of the XXZ spin $1/2$ chain
• Thermodynamic bootstrap program for integrable QFT's: Form factors and correlation functions at finite energy density
• The Second Law of Thermodynamics under Unitary Evolution and External Operations
• A class of states supporting diffusive spin dynamics in the isotropic Heisenberg model
• On the Finite Temperature Formalism in Integrable Quantum Field Theories
• Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems
• Diffusion and signatures of localization in stochastic conformal field theory
• Proposal for measuring the finite-temperature Drude weight of integrable systems
• Form factors of local operators in a one-dimensional two-component Bose gas
• 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
• Spin transport in the XXZ model at high temperatures: Classical dynamics versus quantum S=1/2 autocorrelations
• One-point functions in integrable quantum field theory at finite temperature
• Correlation functions of one-dimensional bosons at low temperature
• Theory of Entropy Production in Quantum Many-Body Systems
• Low temperature dynamics of nonlinear Luttinger liquids
• Emergent entropy production and hydrodynamics in quantum many-body systems
• Spin and magnetothermal transport in the S = 1/2 XXZ chain
• Pulse propagation in interacting one dimensional Bose liquid

Cited by in corpus (156)

• Finite-temperature transport in one-dimensional quantum lattice models
• A Universal Operator Growth Hypothesis
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Lecture notes on Generalised Hydrodynamics
• Generalized hydrodynamics in strongly interacting 1D Bose gases
• Unitary circuits of finite depth and infinite width from quantum channels
• Quantum Generalized Hydrodynamics
• Superdiffusion in spin chains
• Diffusive hydrodynamics from integrability breaking
• Correlation functions and transport coefficients in generalised hydrodynamics
• 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
• Entanglement evolution and generalised hydrodynamics: interacting integrable systems
• Superdiffusion from emergent classical solitons in quantum spin chains
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Kardar-Parisi-Zhang universality from soft gauge modes
• Thermalisation of a trapped one-dimensional Bose gas via diffusion
• Stability of superdiffusion in nearly integrable spin chains
• Fluctuations in ballistic transport from Euler hydrodynamics
• Algebraic construction of current operators in integrable spin chains
• Generalised hydrodynamics with dephasing noise
• 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
• 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
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Ballistic macroscopic fluctuation theory
• Locally quasi-stationary states in noninteracting spin chains
• Current operators in integrable spin chains: lessons from long range deformations
• Generalized hydrodynamics of the KdV soliton gas
• Generalized hydrodynamics regime from the thermodynamic bootstrap program
• Exact description of quantum stochastic models as quantum resistors
• Collision rate ansatz for quantum integrable systems
• The collision rate ansatz for the classical Toda lattice
• Anomalous low-frequency conductivity in easy-plane XXZ spin chains
• Generalized hydrodynamics: a perspective
• Form factors and generalized hydrodynamics for integrable systems
• Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
• Anomalous transport from hot quasiparticles in interacting spin chains
• Hydrodynamics of nonintegrable systems from a relaxation-time approximation
• 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
• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• Generalized Hydrodynamic approach to charge and energy currents in the one-dimensional Hubbard model
• Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation
• Exact real-time longitudinal correlation functions of the massive XXZ chain
• Hydrodynamic gauge fixing and higher order hydrodynamic expansion
• $T\bar{T}$-deformed conformal field theories out of equilibrium
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Exact Thermodynamics and Transport in the Classical Sine-Gordon Model
• Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains
• Generalized hydrodynamics study of the one-dimensional Hubbard model: Stationary clogging and proportionality of spin, charge, and energy currents
• Diffusion and superdiffusion from hydrodynamic projections
• Generalized hydrodynamics in box-ball system
• Microscopic theory of the fluctuating hydrodynamics in nonlinear lattices
• Diffusive Hydrodynamics of Inhomogenous Hamiltonians
• Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains
• Thermal transport in $T\bar{T}$-deformed conformal field theories: from integrability to holography
• Diffusion from Convection
• Thermalization of interacting quasi-one-dimensional systems
• Transport in one-dimensional integrable quantum systems
• Adiabatic formation of bound states in the 1d Bose gas
• Exploiting disorder to probe spin and energy hydrodynamics
• Emergent tracer dynamics in constrained quantum systems
• A converse to Lieb-Robinson bounds in one dimension using index theory
• Entropy growth during free expansion of an ideal gas
• Transport through interacting defects and lack of thermalisation
• Operator front broadening in chaotic and integrable quantum chains
• Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet
• Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
• Linearized regime of the generalized hydrodynamics with diffusion
• Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics
• Hydrodynamics and the eigenstate thermalization hypothesis
• How generalized hydrodynamics time evolution arises from a form factor expansion
• Hydrodynamic Equations for the Toda Lattice
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations
• NMR relaxation in the spin-1 Heisenberg chain
• Integrability breaking in the one dimensional Bose gas: Atomic losses and energy loss
• Quantum Hydrodynamics in Spin Chains with Phase Space Methods
• The dissipative Generalized Hydrodynamic equations and their numerical solution
• Non-Gaussian diffusive fluctuations in Dirac fluids
• Exact large-scale fluctuations of the phase field in the sine-Gordon model
• Scaling of fronts and entanglement spreading during a domain wall melting
• Diffusive hydrodynamics from long-range correlations
• Free energy fluxes and the Kubo-Martin-Schwinger relation
• From dissipationless to normal diffusion in easy-axis Heisenberg spin chain
• Charge-current correlation equalities for quantum systems far from equilibrium
• Corrections to diffusion in interacting quantum systems
• Anisotropic Landau-Lifshitz Model in Discrete Space-Time
• Unusual ergodic and chaotic properties of trapped hard rods
• Popcorn Drude weights from quantum symmetry
• Transport and entanglement across integrable impurities from Generalized Hydrodynamics
• Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem
• Integrability breaking in the Rule 54 cellular automaton
• Integrability breaking from backscattering
• 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
• Universal out-of-equilibrium dynamics of 1D critical quantum systems perturbed by noise coupled to energy
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Hydrodynamic relaxation of spin helices
• On the Hydrodynamics of Unstable Excitations
• Navier-Stokes equations for nearly integrable quantum gases
• Finite temperature spin diffusion in the Hubbard model in the strong coupling limit
• Anomalous current fluctuations from Euler hydrodynamics
• Benchmarks of Generalized Hydrodynamics for 1D Bose Gases
• Semi-classical theory of quantum stochastic resistors
• $T\overline{T}$ deformations and the width of fundamental particles
• Open-system spin transport and operator weight dissipation in spin chains
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• High-low pressure domain wall for the classical Toda lattice
• Undular diffusion in nonlinear sigma models
• The relevant excitations for the one-body function in the Lieb-Liniger model
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain
• Soliton gas of the integrable Boussinesq equation and its generalised hydrodynamics
• The propagator of the finite XXZ spin-$\frac{1}{2}$ chain
• Connected correlations in partitioning protocols: a case study and beyond
• Prethermalization in coupled one-dimensional quantum gases
• The Staircase Model: Massless Flows and Hydrodynamics
• Vanishing and non-vanishing persistent currents of various conserved quantities
• The spin Drude weight of the spin-1/2 $XXZ$ chain: An analytic finite size study
• Identifying diffusive length scales in one-dimensional Bose gases
• On the phase transition in the sublattice TASEP with stochastic blockage
• The Theory of Generalised Hydrodynamics for the One-dimensional Bose Gas
• Experimental Investigation of a Bipartite Quench in a 1D Bose gas
• Emergent Infrared Conformal Dynamics in Strongly Interacting Quantum Gases
• Integrability and charge transport in asymmetric quantum-circuit geometries
• Hidden time-reversal in driven XXZ spin chains: exact solutions and new dissipative phase transitions
• Integrable hydrodynamics of Toda chain: case of small systems
• Emergence of generalized hydrodynamics in the non-local Luttinger model
• Spin Drude weight for the integrable XXZ chain with arbitrary spin
• Emergent random matrix universality in quantum operator dynamics
• Simulating generalised fluids via interacting wave packets evolution
• Finite-temperature transport in the gapped spin-1/2 XXZ chain and one-dimensional lattice spinless fermion model
• Plasmon localization and relaxation, and thermal transport in one-dimensional conductors
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Non-Equilibrium Steady State of the Lieb-Liniger model: exact treatment of the Tonks Girardeau limit
• Scaling of diffusion constants in perturbed easy-axis Heisenberg spin chains
• Quantum fluctuating theory for one-dimensional shock waves
• Anomalous charge transport in the sine-Gordon model
• Finite temperature single-particle Green's function in the Lieb-Liniger model
• A hydrodynamic approach to Stark localization
• Extending the Thermodynamic Form Factor Bootstrap Program: Multiple particle-hole excitations, crossing symmetry, and reparameterization invariance
• Tunable superdiffusion in integrable spin chains using correlated initial states
• Hydrodynamic non-linear response of interacting integrable systems
• Slow transport and bound states for spinless fermions with long-range Coulomb interactions on one-dimensional lattices
• Quantum transport in 1D Hubbard model: Drude weights and Seebeck effect
• Entanglement dynamics of a hard-core quantum gas during a Joule expansion
• A diagrammatic approach towards the thermodynamics of integrable systems