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arXiv · 2110.05972

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

Darren Pereira·Erich J. Mueller
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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.

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Darren Pereira, Erich J. Mueller. 2021-10-12. Dynamics of Spin Helices in the One-Dimensional $XX$ Model. https://doi.org/10.1103/physreva.106.043306

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