Hydrodynamic relaxation of spin helices

Abstract

Motivated by recent cold atom experiments, we study the relaxation of spin helices in quantum XXZ spin chains. The experimentally observed relaxation of spin helices follows scaling laws that are qualitatively different from linear-response transport. We construct a theory of the relaxation of helices, combining generalized hydrodynamics (GHD) with diffusive corrections and the local density approximation. Although helices are far from local equilibrium (so GHD need not apply a priori), our theory reproduces the experimentally observed relaxational dynamics of helices. In particular, our theory explains the existence of temporal regimes with apparent anomalous diffusion, as well as the asymmetry between positive and negative anisotropy regimes.

Typos corrected, references added

References in corpus (22)

• Generalized Thermalization in an Integrable Lattice System
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Dynamical Correlations after a Quantum Quench
• Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-$1/2$ chain
• Superdiffusion in spin chains
• Ballistic spin transport in a periodically driven integrable quantum system
• Superuniversality of superdiffusion
• Thermalisation of a trapped one-dimensional Bose gas via diffusion
• Catching Bethe phantoms and quantum many-body scars: Long-lived spin-helix states in Heisenberg magnets
• Spin crossovers and superdiffusion in the one-dimensional Hubbard model
• Anomalous transport from hot quasiparticles in interacting spin chains
• Kinetic theory of quantum and classical Toda lattices
• Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains
• Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac{1}{2}$ chain
• BBGKY Hierarchy and Generalised Hydrodynamics
• Coexistence of diffusive and ballistic transport in integrable quantum lattice models
• Dynamics of Spin Helices in the One-Dimensional $XX$ Model
• Ballistic transport in integrable quantum chains with degenerate spectra

Cited by in corpus (6)

• Generalized hydrodynamics: a perspective
• The sine-Gordon model from coupled condensates: a Generalized Hydrodynamics viewpoint
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Chiral basis for qubits and spin-helix decay
• Dynamics of spin helices in the diluted one-dimensional $XX$ model
• Universal scaling of higher-order cumulants in quantum isotropic spin chains