Dynamics of Spin Helices in the One-Dimensional $XX$ Model

Abstract

Motivated by cold-atom experiments and a desire to understand far-from-equilibrium quantum transport, we analytically study the dynamics of spin helices in the one-dimensional $XX$ model. We use a Jordan-Wigner transformation to map the spin chain onto a non-interacting Fermi gas with simple equations of motion. The resulting dynamics are nontrivial, however, as the spin-helix initial condition corresponds to a highly nonequilibrium distribution of the fermions. We find a separation of timescales between the in-plane and out-of-plane spin dynamics. We gain insights from analyzing the case of a uniform spin chain and from a semiclassical model. One of our key findings is that the spin correlation functions decay as $t^{-1/2}$ at long time, in contrast to the experimentally observed exponential decay.

arXiv comment10 pages, 6 figures

References in corpus (19)

• Unpaired Majorana fermions in quantum wires
• Feshbach Resonances in Ultracold Gases
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Generalized Gibbs ensemble in integrable lattice models
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Generalized HydroDynamics on an Atom Chip
• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles
• Large-scale description of interacting one-dimensional Bose gases: generalized hydrodynamics supersedes conventional hydrodynamics
• Full counting statistics in a propagating quantum front and random matrix spectra
• Generalized hydrodynamics in strongly interacting 1D Bose gases
• Generalized Jordan-Wigner Transformations
• Quantum Generalized Hydrodynamics
• Dynamic scaling of fronts in the quantum XX chain
• Transverse spin dynamics in the anisotropic Heisenberg model realized with ultracold atoms
• Exact large deviation function of spin current for the one dimensional XX spin chain with domain wall initial condition
• Spin Gap in Chains with Hidden Symmetries
• Numerical Jordan-Wigner approach for two dimensional spin systems

Cited by in corpus (8)

• Hydrodynamic relaxation of spin helices
• Universality in relaxation of spin helices under the $XXZ$- spin chain dynamics
• Optimal remote restoring of quantum states in communication lines via local magnetic field
• Chiral basis for qubits and spin-helix decay
• Dynamics of spin helices in the diluted one-dimensional $XX$ model
• Predictive complexity of quantum subsystems
• Universal scaling of higher-order cumulants in quantum isotropic spin chains
• Fermionic Approach to Elementary Excitations and Magnetization Plateaus in an S=1/2 XX Hybrid Trimer-Dimer Chain