Hydrodynamics of spin transport in the Haldane-Shastry chain
arXiv:2407.08727 · doi:10.1103/PhysRevB.110.195439
Abstract
We use kinetic theory and the thermodynamic Bethe ansatz to derive the hydrodynamics of spin transport in the Haldane-Shastry chain. We obtain analytical expressions for relaxation from weak-domain-wall initial conditions and corresponding predictions for the spin Drude weight. We corroborate the latter against an exact microscopic calculation at infinite temperature and Luttinger-liquid expectations at zero temperature. We further obtain an analytical expression for the long-wavelength dynamics of the longitudinal spin structure factor at all fillings and temperatures. We show that the latter interpolates between an empirically exact expression that we have found at infinite temperature and the long-wavelength limit of the Haldane-Zirnbauer formula at zero temperature.
arXiv commentv2: 15 pages, 2 figures, minor revisions and close to published version
References in corpus (42)
- Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
- Emergent hydrodynamics in integrable quantum systems out of equilibrium
- Transport and conservation laws
- Finite-temperature transport in one-dimensional quantum lattice models
- Spin transport in a one-dimensional anisotropic Heisenberg model
- Hydrodynamic Diffusion in Integrable Systems
- Time-evolving a matrix product state with long-ranged interactions
- Non-zero temperature transport near quantum critical points
- 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
- Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
- Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
- Physics and Mathematics of Calogero particles
- Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
- Microscopic origin of ideal conductivity in integrable quantum models
- Kinetic equation for a dense soliton gas
- Conservation laws, integrability and transport in one-dimensional quantum systems
- Drude Weight for the Lieb-Liniger Bose Gas
- Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin- chain
- Superdiffusion in spin chains
- Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
- Superuniversality of superdiffusion
- Generalised hydrodynamics of the classical Toda system
- Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons
- Superdiffusion from emergent classical solitons in quantum spin chains
- Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
- Kardar-Parisi-Zhang universality from soft gauge modes
- Full counting statistics in the Haldane-Shastry chain
- Interacting and noninteracting integrable systems
- Expansion potentials for exact far-from-equilibrium spreading of particles and energy
- Subdiffusive front scaling in interacting integrable models
- Kinetic theory of quantum and classical Toda lattices
- Integrals of motion of the Haldane Shastry Model
- Is there an attraction between spinons in the Haldane--Shastry model?
- Dynamical T=0 correlations of the S=1/2 1D Heisenberg Anti-Ferromagnet with 1/r^2 exchange in a magnetic field
- A Note on Dressed S-Matrices in Models with Long-Range Interactions
- Coordinate Representation of the Two-Spinon wavefunction and Spinon Interaction
- Hydrodynamic equations for the Ablowitz-Ladik discretization of the nonlinear Schroedinger equation
- BBGKY Hierarchy and Generalised Hydrodynamics
- Thermodynamics of Inozemtsev's Elliptic Spin Chain
- Particle Scattering and Fusion for the Ablowitz-Ladik Chain