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

TL;DR

This paper investigates how immobile holes affect the quantum dynamics of spin helices in a one-dimensional $XX$ model, revealing decay and persistent oscillations depending on hole density, and validates a numerical method for broader models.

Contribution

It provides an exact analytical approach to study spin helix dynamics with holes and validates a matrix product state technique for more complex models.

Findings

Small hole densities lead to exponential decay of spin helices.

Large hole densities result in persistent oscillations.

The analytical results match experimental observations at low hole densities.

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.