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.
v2: 15 pages, 2 figures, minor revisions and close to published version
References in corpus (14)
- Spin transport in a one-dimensional anisotropic Heisenberg model
- Time-evolving a matrix product state with long-ranged interactions
- Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
- Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
- Physics and Mathematics of Calogero particles
- Conservation laws, integrability and transport in one-dimensional quantum systems
- Superdiffusion in 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
- Kinetic theory of quantum and classical Toda lattices
- Hydrodynamic equations for the Ablowitz-Ladik discretization of the nonlinear Schroedinger equation
- BBGKY Hierarchy and Generalised Hydrodynamics
- Particle Scattering and Fusion for the Ablowitz-Ladik Chain