Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains

Abstract

We address spin transport in the easy-axis Heisenberg spin chain subject to integrability-breaking perturbations. We find that spin transport is subdiffusive with dynamical exponent $z=4$ up to a timescale that is parametrically long in the anisotropy. In the limit of infinite anisotropy, transport is subdiffusive at all times; for large finite anisotropy, one eventually recovers diffusion at late times, but with a diffusion constant independent of the strength of the integrability breaking perturbation. We provide numerical evidence for these findings, and explain them by adapting the generalized hydrodynamics framework to nearly integrable dynamics. Our results show that the diffusion constant of near-integrable interacting spin chains is generically not perturbative in the integrability breaking strength.

4+epsilon pages + 4 pages supp. mat. v2: updated figures

References in corpus (23)

• The density-matrix renormalization group in the age of matrix product states
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Microwave-engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms
• Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-$1/2$ chain
• Superdiffusion in spin chains
• Correlation functions and transport coefficients in generalised hydrodynamics
• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Superuniversality of superdiffusion
• Hydrodynamics of weak integrability breaking
• Thermalization and light cones in a model with weak integrability breaking
• Tomonaga-Luttinger Liquid Behavior and Spinon Confinement in YbAlO${}_3$
• Universality in the onset of quantum chaos in many-body systems
• Thermalisation of a trapped one-dimensional Bose gas via diffusion
• The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties
• Stability of superdiffusion in nearly integrable spin chains
• Subdiffusion and many-body quantum chaos with kinetic constraints
• The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges
• Form factors and generalized hydrodynamics for integrable systems
• Fragmentation and emergent integrable transport in the weakly tilted Ising chain
• A Yang-Baxter integrable cellular automaton with a four site update rule
• Macroscopic effects of localised measurements in jammed states of quantum spin chains
• Emergent Fracton Dynamics in a Non-Planar Dimer Model
• Less is more: more scattering leading to less resistance

Cited by in corpus (20)

• Generalized hydrodynamics: a perspective
• Anomalous transport from hot quasiparticles in interacting spin chains
• Distinct universality classes of diffusive transport from full counting statistics
• Rise and fall, and slow rise again, of operator entanglement under dephasing
• Emergent tracer dynamics in constrained quantum systems
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Probing spin hydrodynamics on a superconducting quantum simulator
• Measurement catastrophe and ballistic spread of charge density with vanishing current
• Spin diffusion in perturbed isotropic Heisenberg spin chain
• From dissipationless to normal diffusion in easy-axis Heisenberg spin chain
• Integrability breaking from backscattering
• Open-system spin transport and operator weight dissipation in spin chains
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• Thouless approach in transport in integrable and perturbed easy-axis Heisenberg chains
• 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
• Thermal Drude weight in an integrable chiral clock model
• Nontrivial damping of magnetization currents in perturbed spin chains
• Subdiffusive Energy Transport and Antipersistent Correlations Due to the Scattering of Phonons and Discrete Breathers
• Transport in a System with a Tower of Quantum Many-Body Scars