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

TL;DR

This paper analytically investigates the non-equilibrium dynamics of spin helices in the one-dimensional XX model, revealing a power-law decay of correlations and providing insights relevant to cold-atom experiments.

Contribution

It introduces an analytical approach to study spin helix dynamics in the XX model, highlighting a separation of timescales and contrasting decay behaviors with experimental results.

Findings

Spin correlation functions decay as t^{-1/2} at long times.

Identifies a separation of timescales between in-plane and out-of-plane spin dynamics.

Provides a semiclassical interpretation of the nontrivial dynamics.

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.