Dynamics of Spin Helices in the 1D XX Model
Abstract
Motivated by cold atom experiments, we analytically study the dynamics of spin helices in the 1D XX model. Using the JordanWigner transformation to map spins into fermions, we calculate the evolution of the spin helix over time. The fermions are noninteracting, with simple equations of motion. Nonetheless, the calculation is nontrivial, as the spinhelix initial condition corresponds to a highly nonequilibrium distribution of the fermions. We compare the resulting dynamics to a semiclassical model, and find qualitatively similar outofplane dynamics. The inplane dynamics, however, are dramatically different. The spins decohere over time, resulting in a $t^{1/2}$ decay of the spinspin correlation function, which can be contrasted to exponential decay seen in recent experiments.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.05972
 Bibcode:
 2021arXiv211005972P
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Quantum Gases;
 Quantum Physics
 EPrint:
 6 pages, 6 figures