Superdiffusion in spin chains

Abstract

This review summarizes recent advances in our understanding of anomalous transport in spin chains, viewed through the lens of integrability. Numerical advances, based on tensor-network methods, have shown that transport in many canonical integrable spin chains -- most famously the Heisenberg model -- is anomalous. Concurrently, the framework of generalized hydrodynamics has been extended to explain some of the mechanisms underlying anomalous transport. We present what is currently understood about these mechanisms, and discuss how they resemble (and differ from) the mechanisms for anomalous transport in other contexts. We also briefly review potential transport anomalies in systems where integrability is an emergent or approximate property. We survey instances of anomalous transport and dynamics that remain to be understood.

arXiv commentv2: published version. Review article, 73 pages, 8 figures

References in corpus (193)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Luttinger Liquid Behavior in Carbon Nanotubes
• Renormalization Group Approach to Interacting Fermions
• Time-dependent variational principle for quantum lattices
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Generalized Gibbs ensemble in integrable lattice models
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Transport and conservation laws
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Classical/quantum integrability in AdS/CFT
• Finite-temperature transport in one-dimensional quantum lattice models
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Generalized HydroDynamics on an Atom Chip
• Hydrodynamic Diffusion in Integrable Systems
• Quasilocal charges in integrable lattice systems
• The Fascinating World of Landau-Lifshitz-Gilbert Equation: An Overview
• Non-zero temperature transport near quantum critical points
• 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
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Exact scaling functions for one-dimensional stationary KPZ growth
• Real-time dynamics in spin-1/2 chains with adaptive time-dependent DMRG
• Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
• New Exactly Solvable Model of Strongly Correlated Electrons Motivated by High T_c Superconductivity
• Diffusion and ballistic transport in one-dimensional quantum systems
• Families of quasi-local conservation laws and quantum spin transport
• Prethermalization and thermalization in models with weak integrability breaking
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Solvable Hydrodynamics of Quantum Integrable Systems
• Integrability and ideal conductance at finite temperatures
• 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
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
• Exact results for anomalous transport in one dimensional Hamiltonian systems
• Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles
• Microscopic origin of ideal conductivity in integrable quantum models
• Rare region effects and dynamics near the many-body localization transition
• Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains
• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• Lecture notes on Generalised Hydrodynamics
• 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
• Zero-frequency transport properties of one dimensional spin-1/2 systems
• Electron Spin Resonance in S=1/2 antiferromagnetic chains
• Full counting statistics in a propagating quantum front and random matrix spectra
• Integral representations for correlation functions of the XXZ chain at finite temperature
• Super-diffusion in one-dimensional quantum lattice models
• Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures
• Thermodynamics of the Spin Luttinger-Liquid in a Model Ladder Material
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• Low energy effective Hamiltonian for the XXZ spin chain
• Quench Dynamics in a Model with Tuneable Integrability Breaking
• Spin Transport in a Mott Insulator of Ultracold Fermions
• Low temperature relaxational dynamics of the Ising chain in a transverse field
• Drude Weight for the Lieb-Liniger Bose Gas
• Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
• Evidence for ideal insulating/conducting state in a 1D integrable system
• Entanglement and matrix elements of observables in interacting integrable systems
• Prethermalization and Thermalization in Isolated Quantum Systems
• Conductivity of a clean one-dimensional wire
• Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains
• Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain
• Algebraic Curve for the SO(6) sector of AdS/CFT
• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
• Real-time and real-space spin- and energy dynamics in one-dimensional spin-1/2 systems induced by local quantum quenches at finite temperatures
• Redundancies in Nambu-Goldstone Bosons
• Integrable Trotterization: Local Conservation Laws and Boundary Driving
• Fibonacci family of dynamical universality classes
• Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-$1/2$ chain
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Dynamics of composite Haldane spin chains in IPA-CuCl3
• Low temperature spin diffusion in the one-dimensional quantum $O(3)$ nonlinear $\sigma$-model
• On the finite temperature Drude weight of the anisotropic Heisenberg chain
• Diffusive hydrodynamics from integrability breaking
• Ballistic spin transport in a periodically driven integrable quantum system
• Anomalous spin diffusion in one-dimensional antiferromagnets
• Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Relaxation dynamics in the gapped XXZ spin-1/2 chain
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• Strong Evidence of Normal Heat Conduction in a one-Dimensional Quantum System
• Far-from-equilibrium field theory of many-body quantum spin systems: Prethermalization and relaxation of spin spiral states in three dimensions
• The Yangian symmetry of the Hubbard Model
• Superdiffusion from emergent classical solitons in quantum spin chains
• String-charge duality in integrable lattice models
• Correlation functions of integrable models: a description of the ABACUS algorithm
• Low-temperature transport in Heisenberg chains
• Thermal Conductivity of Spin-1/2 Chains
• Kardar-Parisi-Zhang universality from soft gauge modes
• Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
• Exactly conserved quasilocal operators for the XXZ spin chain
• Exact Drude weight for the one-dimensional Hubbard model at finite temperatures
• Stability of superdiffusion in nearly integrable spin chains
• Band and correlated insulators of cold fermions in a mesoscopic lattice
• Non-equilibrium DC noise in a Luttinger liquid with impurity
• Kardar-Parisi-Zhang Scaling for an Integrable Lattice Landau-Lifshitz Spin Chain
• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Quantum information scrambling after a quantum quench
• Finite-temperature Drude weight within the anisotropic Heisenberg chain
• Energy transport between two integrable spin chains
• Thermodyamic bounds on Drude weights in terms of almost-conserved quantities
• Diffusive high-temperature transport in the one-dimensional Hubbard model
• Generalised hydrodynamics with dephasing noise
• Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice
• Haldane Gapped Spin Chains: Exact Low Temperature Expansions of Correlation Functions
• Dynamics and Transport at the Threshold of Many-Body Localization
• Incomplete thermalization from trap-induced integrability breaking: lessons from classical hard rods
• Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
• 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
• Heavy Operators and Hydrodynamic Tails
• 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
• Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories
• Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
• Domain-wall melting in the spin-$1/2$ XXZ spin chain: emergent Luttinger liquid with fractal quasi-particle charge
• Macroscopic Diffusive Transport in a Microscopically Integrable Hamiltonian System
• Thermal form-factor approach to dynamical correlation functions of integrable lattice models
• Non-local emergent hydrodynamics in a long-range quantum spin system
• Theory of Nuclear Magnetic Relaxation in Haldane Gap Antiferromagnets
• Hydrodynamics in lattice models with continuous non-Abelian symmetries
• Optical Conductivity of Clean Metals
• Transport in a one-dimensional isotropic Heisenberg model at high temperature
• Interacting and noninteracting integrable systems
• The spin Drude weight of the XXZ chain and generalized hydrodynamics
• 2D Superexchange mediated magnetization dynamics in an optical lattice
• Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
• Generalized hydrodynamics regime from the thermodynamic bootstrap program
• Integrable sigma models with theta=pi
• Collision rate ansatz for quantum integrable systems
• Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point
• Drude weight in systems with open boundary conditions
• Scaling of electrical and thermal conductivities in an almost integrable chain
• Subdiffusive front scaling in interacting integrable models
• Anomalous low-frequency conductivity in easy-plane XXZ spin chains
• Expansion potentials for exact far-from-equilibrium spreading of particles and energy
• Bloch Walls and Macroscopic String States in Bethe's solution of the Heisenberg Ferromagnetic Linear Chain
• Heat conductivity of the Heisenberg spin-1/2 ladder: From weak to strong breaking of integrability
• Hydrodynamics of nonintegrable systems from a relaxation-time approximation
• Time-dependent matrix product ansatz for interacting reversible dynamics
• Spin transport properties of the quantum one-dimensional non-linear sigma model : an application to Haldane gap systems
• Density form factors of the 1D Bose gas for finite entropy states
• 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
• Integrable sigma models and perturbed coset models
• Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain
• A class of states supporting diffusive spin dynamics in the isotropic Heisenberg model
• Sigma models as perturbed conformal field theories
• Diffusive transport in spin-1 chains at high temperatures
• Free fermions at the edge of interacting systems
• Decay of fermionic quasiparticles in one-dimensional quantum liquids
• Long-Time Tails, Weak Localization, and Classical and Quantum Critical Behavior
• Quantum Stability for the Heisenberg Ferromagnet
• Superdiffusive transport of energy in one-dimensional metals
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains
• Integrable spin chains with random interactions
• Ballistic transport and boundary resistances in inhomogeneous quantum spin chains
• Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures
• Spin and energy correlations in the one dimensional spin 1/2 Heisenberg model
• Diffusion from Convection
• Transport in one-dimensional integrable quantum systems
• Magnetization and energy dynamics in spin ladders: Evidence of diffusion in time, frequency, position, and momentum
• Quasi-soliton scattering in quantum spin chains
• Decay of spin-spin correlations in disordered quantum and classical spin chains
• Quantum Crystals and Spin Chains
• Magnetization dynamics in clean and disordered spin-1 XXZ chains
• Quantum criticality in Ising chains with random hyperuniform couplings
• Giant Magnons and Singular Curves
• Revisiting the Mazur bound and the Suzuki equality
• Charge diffusion in the one-dimensional Hubbard model
• Integrability breaking in the one dimensional Bose gas: Atomic losses and energy loss
• NMR relaxation in the spin-1 Heisenberg chain
• The equilibrium landscape of the Heisenberg spin chain
• Domain wall melting in spin-1 chains
• Ballistic transport in integrable quantum chains with degenerate spectra
• Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz
• Finite-size anomalies of the Drude weight: role of symmetries and ensembles
• On self-similar solutions of the vortex filament equation
• Undular diffusion in nonlinear sigma models
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain

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• Approximation theory for Green's functions via the Lanczos algorithm
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