Dynamics of spin helices in the diluted one-dimensional $XX$ model

Abstract

Motivated by discrepancies between recent cold atom experiments and the associated theory, we explore the effect of immobile holes on the quantum dynamics of $x$-$z$ spin helices in the one-dimensional $XX$ model. We calculate the exact spin dynamics by mapping onto a system of non-interacting fermions, averaging over the distribution of holes. At small hole densities we find that the helical spin pattern decays exponentially, with a pitch dependence that agrees with the experiments. At large hole densities we instead find persistent oscillations. While our analytic approach does not generalize to the $XXZ$ model with arbitrary anisotropies, we validate a matrix product state technique which might be used to model the experiments in those settings.

10 pages, 8 figures

References in corpus (18)

• The density-matrix renormalization group in the age of matrix product states
• The ITensor Software Library for Tensor Network Calculations
• Unifying time evolution and optimization with matrix product states
• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Finite-temperature transport in one-dimensional quantum lattice models
• Finite Temperature Density Matrix Renormalization using an enlarged Hilbert space
• Spin diffusion from an inhomogeneous quench in an integrable system
• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Colloquium: Atomic spin chains on surfaces
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Catching Bethe phantoms and quantum many-body scars: Long-lived spin-helix states in Heisenberg magnets
• Transverse spin dynamics in the anisotropic Heisenberg model realized with ultracold atoms
• Enhanced Superexchange in a Tilted Mott Insulator
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Dynamics of Spin Helices in the One-Dimensional $XX$ Model
• Hydrodynamic relaxation of spin helices

Cited by in corpus (1)

• Universal scaling of higher-order cumulants in quantum isotropic spin chains