Anomalous transport from hot quasiparticles in interacting spin chains

Abstract

Many experimentally relevant quantum spin chains are approximately integrable, and support long-lived quasiparticle excitations. A canonical example of integrable model of quantum magnetism is the XXZ spin chain, for which energy spreads ballistically, but, surprisingly, high-temperature spin transport can be diffusive or superdiffusive. We review the transport properties of this model using an intuitive quasiparticle picture that relies on the recently introduced framework of generalized hydrodynamics. We discuss how anomalous linear response properties emerge from hierarchies of quasiparticles both in integrable and near-integrable limits, with an emphasis on the role of hydrodynamic fluctuations. We also comment on recent developments including non-linear response, full-counting statistics and far-from-equilibrium transport. We provide an overview of recent numerical and experimental results on transport in XXZ spin chains.

arXiv comment48 pages, 7 figures. Invited review article for Reports on Progress in Physics. Comments welcome

References in corpus (155)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• The density-matrix renormalization group in the age of matrix product states
• Nonequilibrium dynamics of closed interacting quantum systems
• Efficient classical simulation of slightly entangled quantum computations
• A Quantum Engineer's Guide to Superconducting Qubits
• The large deviation approach to statistical mechanics
• Many-body localization, thermalization, and entanglement
• Efficient simulation of one-dimensional quantum many-body systems
• NMR Techniques for Quantum Control and Computation
• Electron Counting Statistics and Coherent States of Electric Current
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• 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
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Full Counting Statistics of Charge Transfer in Coulomb Blockade Systems
• Finite-temperature transport in one-dimensional quantum lattice models
• Generalized HydroDynamics on an Atom Chip
• Hydrodynamic Diffusion in Integrable Systems
• Quasilocal charges in integrable lattice systems
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• 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
• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Soliton gases and generalized hydrodynamics
• Exact scaling functions for one-dimensional stationary KPZ growth
• Fracton hydrodynamics
• Families of quasi-local conservation laws and quantum spin transport
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Solvable Hydrodynamics of Quantum Integrable Systems
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Large-scale description of interacting one-dimensional Bose gases: generalized hydrodynamics supersedes conventional hydrodynamics
• Microscopic origin of ideal conductivity in integrable quantum models
• Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains
• Lecture notes on Generalised Hydrodynamics
• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• Analytic solution of the Domain Wall non-equilibrium stationary state
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
• Super-diffusion in one-dimensional quantum lattice models
• Generalized hydrodynamics in strongly interacting 1D Bose gases
• Microwave-engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms
• A note on generalized hydrodynamics: inhomogeneous fields and other concepts
• Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures
• Dynamics of hard rods with initial domain wall state
• A geometric viewpoint on generalized hydrodynamics
• Quantum Generalized Hydrodynamics
• Subdiffusion and heat transport in a tilted 2D Fermi-Hubbard system
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Aspects of non-equilibrium in classical and quantum systems: slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics
• Drude Weight for the Lieb-Liniger Bose Gas
• Generalized hydrodynamics with space-time inhomogeneous interactions
• Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain
• Integrable Trotterization: Local Conservation Laws and Boundary Driving
• Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
• Experimental Observation of Bethe Strings
• Interaction-controlled transport of an ultracold Fermi gas
• Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-$1/2$ chain
• Entanglement evolution and generalised hydrodynamics: noninteracting systems
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Superdiffusion in spin chains
• Quantum dynamics of thermalizing systems
• Low temperature spin diffusion in the one-dimensional quantum $O(3)$ nonlinear $\sigma$-model
• Universal Statistics of Transport in Disordered Conductors
• Diffusive hydrodynamics from integrability breaking
• Ballistic spin transport in a periodically driven integrable quantum system
• Correlation functions and transport coefficients in generalised hydrodynamics
• Anomalous Subdiffusion from Subsystem 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
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics
• Extension of the Generalized Hydrodynamics to the Dimensional Crossover Regime
• Superuniversality of superdiffusion
• Non-Equilibrium Dynamics and Weakly Broken Integrability
• Generalised hydrodynamics of the classical Toda system
• Hydrodynamics of weak integrability breaking
• Exact large-scale correlations in integrable systems out of equilibrium
• 17O NMR study of q=0 spin excitations in a nearly ideal S=1/2 1D Heisenberg antiferromagnet, Sr2CuO3, up to 800 K
• Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup
• Superdiffusion from emergent classical solitons in quantum spin chains
• String-charge duality in integrable lattice models
• Entanglement evolution and generalised hydrodynamics: interacting integrable systems
• Kardar-Parisi-Zhang universality from soft gauge modes
• The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties
• Thermalisation of a trapped one-dimensional Bose gas via diffusion
• 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
• Universal relaxational dynamics of gapped one dimensional models in the quantum sine-Gordon universality class
• Algebraic construction of current operators in integrable spin chains
• Full Counting Statistics in the Transverse Field Ising Chain
• Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics
• Transport fluctuations in integrable models out of equilibrium
• Spin transport in the XXZ chain at finite temperature and momentum
• 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
• Emergent prethermalization signatures in out-of-time ordered correlations
• 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
• Lower Bounding Diffusion Constant by the Curvature of Drude Weight
• Exact anomalous current fluctuations in a deterministic interacting model
• Subdiffusion and many-body quantum chaos with kinetic constraints
• Universality classes of spin transport in one-dimensional isotropic magnets: the onset of logarithmic anomalies
• Energy transport in an integrable parafermionic chain via generalized hydrodynamics
• Spin crossovers and superdiffusion in the one-dimensional Hubbard model
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Macroscopic Diffusive Transport in a Microscopically Integrable Hamiltonian System
• Universal broadening of the light cone in low-temperature transport
• The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges
• Hydrodynamics in lattice models with continuous non-Abelian symmetries
• Onset of many-body quantum chaos due to breaking integrability
• Integrability of a deterministic cellular automaton driven by stochastic boundaries
• Current operators in integrable spin chains: lessons from long range deformations
• Weak integrability breaking: chaos with integrability signature in coherent diffusion
• Absence of Normal Fluctuations in an Integrable Magnet
• The spin Drude weight of the XXZ chain and generalized hydrodynamics
• Full counting statistics in the spin-1/2 Heisenberg XXZ chain
• On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems
• Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
• Low-Temperature Transport in Out-of-Equilibrium XXZ Chains
• Anomalous low-frequency conductivity in easy-plane XXZ spin chains
• Heat conductivity of the Heisenberg spin-1/2 ladder: From weak to strong breaking of integrability
• Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models
• Integrable Matrix Models in Discrete Space-Time
• Generalized Hydrodynamic approach to charge and energy currents in the one-dimensional Hubbard model
• Kinetic theory of quantum and classical Toda lattices
• A Yang-Baxter integrable cellular automaton with a four site update rule
• Simulation of quantum many-body dynamics with Tensor Processing Units: Floquet prethermalization
• Long-Time Tails, Weak Localization, and Classical and Quantum Critical Behavior
• Anomalous Dynamics and Equilibration in the Classical Heisenberg Chain
• 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
• Diffusion and superdiffusion from hydrodynamic projections
• Dynamics of large deviations in the hydrodynamic limit: Non-interacting systems
• Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains
• Euler-scale dynamical correlations in integrable systems with fluid motion
• Diffusion from Convection
• Emergent tracer dynamics in constrained quantum systems
• Spin hydrodynamics in the S = 1/2 anisotropic Heisenberg chain
• Quasi-conserved charges in the perturbed spin-1/2 XXX model
• The GGE averaged currents of the classical Toda chain
• Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet
• NMR relaxation in the spin-1 Heisenberg chain
• Absence of superdiffusion in certain random spin models
• Coexistence of diffusive and ballistic transport in integrable quantum lattice models
• Anisotropic Landau-Lifshitz Model in Discrete Space-Time
• Multiple relaxation times in perturbed XXZ chain
• Inhomogeneous spin excitations in weakly coupled spin-1/2 chains

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• Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
• Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator
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• Weak integrability breaking perturbations of integrable models
• Dynamical criticality of magnetization transfer in integrable spin chains
• Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Non-Gaussian diffusive fluctuations in Dirac fluids
• Slow crossover from superdiffusion to diffusion in isotropic spin chains
• Parametrically long lifetime of superdiffusion in non-integrable spin chains
• Hydrodynamic relaxation of spin helices
• Efficient computation of cumulant evolution and full counting statistics: application to infinite temperature quantum spin chains
• Quantum turnstiles for robust measurement of full counting statistics
• Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers
• Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission
• Diffusive hydrodynamics of hard rods from microscopics
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• Finding local integrals of motion in quantum lattice models in the thermodynamic limit
• Spin Drude weight for the integrable XXZ chain with arbitrary spin
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Dynamic scaling and Family-Vicsek universality in $SU(N)$ quantum spin chains
• Ising spin-1/2 XXZ chain's quantum problems beyond the spinon paradigm
• Energy dynamics in a class of local random matrix Hamiltonians
• Tunable superdiffusion in integrable spin chains using correlated initial states
• Universal scaling of higher-order cumulants in quantum isotropic spin chains
• Boundary-driven magnetization transport in the spin-$1/2$ XXZ chain: Role of the system-bath coupling strength and timescales
• Anomalous Quantum Relaxation in the Infinite Temperature Hubbard Chain