Stability of superdiffusion in nearly integrable spin chains

Abstract

Superdiffusive finite-temperature transport has been recently observed in a variety of integrable systems with nonabelian global symmetries. Superdiffusion is caused by giant Goldstone-like quasiparticles stabilized by integrability. Here, we argue that these giant quasiparticles remain long-lived, and give divergent contributions to the low-frequency conductivity $\sigma (\omega )$, even in systems that are not perfectly integrable. We find, perturbatively, that $\sigma (\omega )\sim {\omega }^{-1/3}$ for translation-invariant static perturbations that conserve energy, and $\sigma (\omega )\sim |\log \omega |$ for noisy perturbations. The (presumable) crossover to regular diffusion appears to lie beyond low-order perturbation theory. By contrast, integrability-breaking perturbations that break the nonabelian symmetry yield conventional diffusion. Numerical evidence supports the distinction between these two classes of perturbations.

arXiv comment4 + epsilon pages, 2 figures + 8 pages supp. mat. v3: published version

References in corpus (82)

• Thermalization and its mechanism for generic isolated quantum systems
• 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
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Experimental Observation of a Generalized Gibbs Ensemble
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Finite-temperature transport in one-dimensional quantum lattice models
• Matrix product operator representations
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Generalized HydroDynamics on an Atom Chip
• Hydrodynamic Diffusion in Integrable Systems
• Time-evolving a matrix product state with long-ranged interactions
• Spin diffusion from an inhomogeneous quench in an integrable system
• 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
• Diffusion and ballistic transport in one-dimensional quantum systems
• Prethermalization and thermalization in models with weak integrability breaking
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• 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
• Large-scale description of interacting one-dimensional Bose gases: generalized hydrodynamics supersedes conventional hydrodynamics
• Microscopic origin of ideal conductivity in integrable quantum models
• Operator space entanglement entropy in transverse Ising chain
• 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
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Analytic solution of the Domain Wall non-equilibrium stationary state
• Super-diffusion in one-dimensional quantum lattice models
• 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
• Quantum Generalized Hydrodynamics
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Drude Weight for the Lieb-Liniger Bose Gas
• Bosonic Excitations in Random Media
• Is efficiency of classical simulations of quantum dynamics related to integrability?
• Prethermalization and Thermalization in Isolated Quantum Systems
• Generalized hydrodynamics with space-time inhomogeneous interactions
• Real-time and real-space spin- and energy dynamics in one-dimensional spin-1/2 systems induced by local quantum quenches at finite temperatures
• Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-$1/2$ chain
• Quantum dynamics of thermalizing systems
• Low temperature spin diffusion in the one-dimensional quantum $O(3)$ nonlinear $\sigma$-model
• Diffusive hydrodynamics from integrability breaking
• Anomalous spin diffusion in one-dimensional antiferromagnets
• Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
• Extension of the Generalized Hydrodynamics to the Dimensional Crossover Regime
• Superuniversality of superdiffusion
• Reducing the numerical effort of finite-temperature density matrix renormalization group transport calculations
• Superdiffusion from emergent classical solitons in quantum spin chains
• Kardar-Parisi-Zhang universality from soft gauge modes
• Thermalisation of a trapped one-dimensional Bose gas via diffusion
• Quantum thermalization dynamics with Matrix-Product States
• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Algebraic construction of current operators in integrable spin chains
• Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics
• Generalised hydrodynamics with dephasing noise
• Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
• Incomplete thermalization from trap-induced integrability breaking: lessons from classical hard rods
• 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
• Hydrodynamics in lattice models with continuous non-Abelian symmetries
• Weak integrability breaking: chaos with integrability signature in coherent diffusion
• Scaling of electrical and thermal conductivities in an almost integrable chain
• Anomalous low-frequency conductivity in easy-plane XXZ spin chains
• Particle-hole pairs and density-density correlations in the Lieb-Liniger model
• Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models
• Optimized Lie-Trotter-Suzuki decompositions for two and three non-commuting terms
• Superdiffusive transport of energy in one-dimensional metals
• Ballistic transport and boundary resistances in inhomogeneous quantum spin chains
• A TBA description of thermal transport in the XXZ Heisenberg model
• Anomalous and regular transport in spin 1/2 chains: AC conductivity
• Dissipation-assisted operator evolution method for capturing hydrodynamic transport
• Integrability breaking in the one dimensional Bose gas: Atomic losses and energy loss
• Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem

Cited by in corpus (61)

• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Superdiffusion in spin chains
• Hydrodynamics of weak integrability breaking
• Onset of many-body quantum chaos due to breaking integrability
• Correlations and commuting transfer matrices in integrable unitary circuits
• Noncommuting conserved charges in quantum thermodynamics and beyond
• Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models
• Anomalous transport from hot quasiparticles in interacting spin chains
• Generalized hydrodynamics: a perspective
• Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
• Unbounded entanglement production via a dissipative impurity
• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• Weak integrability breaking perturbations of integrable models
• Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit
• Anomalous Dynamics and Equilibration in the Classical Heisenberg Chain
• Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains
• Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain
• Thermalization of interacting quasi-one-dimensional systems
• Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
• Liouvillian Dynamics of the Open Schwinger Model: String Breaking and Kinetic Dissipation in a Thermal Medium
• Exploiting disorder to probe spin and energy hydrodynamics
• Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation
• Absence of superdiffusion in certain random spin models
• Universal scaling of spin mixing dynamics in a strongly interacting one-dimensional Fermi gas
• Spin diffusion in perturbed isotropic Heisenberg spin chain
• Nonequilibrium criticality driven by Kardar-Parisi-Zhang fluctuations in the synchronization of oscillator lattices
• A $\frac{1}{3}$ power-law universality class out of stochastic driving in interacting systems
• Coexistence of diffusive and ballistic transport in integrable quantum lattice models
• From dissipationless to normal diffusion in easy-axis Heisenberg spin chain
• Long-lived Solitons and Their Signatures in the Classical Heisenberg Chain
• Slow crossover from superdiffusion to diffusion in isotropic spin chains
• Parametrically long lifetime of superdiffusion in non-integrable spin chains
• Effective dissipation rate in a Liouvillian graph picture of high-temperature quantum hydrodynamics
• Integrability breaking from backscattering
• Efficient computation of cumulant evolution and full counting statistics: application to infinite temperature quantum spin chains
• Long-living prethermalization in nearly integrable spin ladders
• Adiabatic gauge potential and integrability breaking with free fermions
• Quantum turnstiles for robust measurement of full counting statistics
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• Open-system spin transport and operator weight dissipation in spin chains
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Real-time broadening of bath-induced density profiles from closed-system correlation functions
• Coexistence of directed momentum current and ballistic energy diffusion in coupled non-Hermitian kicked rotors
• Superdiffusive transport on lattices with nodal impurities
• Breakdown of superdiffusion in perturbed quantum integrable spin chains and ladders
• Diffusive charge transport in the gapped 1D Hubbard model at all finite temperatures
• Integrability of Goldilocks quantum cellular automata
• Emergent random matrix universality in quantum operator dynamics
• Noise Induced Universal Diffusive Transport in Fermionic Chains
• Thouless approach in transport in integrable and perturbed easy-axis Heisenberg chains
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Scaling of diffusion constants in perturbed easy-axis Heisenberg spin chains
• Macroproperties vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models
• A theory of quasiballistic spin transport
• Superdiffusion resilience in Heisenberg Chains with 2D interactions on a quantum processor
• Superdiffusive transport in chaotic quantum systems with nodal interactions
• Transport in a System with a Tower of Quantum Many-Body Scars
• Operator entanglement in $\mathrm{SU}(2)$-symmetric dissipative quantum many-body dynamics
• Nontrivial damping of magnetization currents in perturbed spin chains