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

• URL: http://arxiv.org/abs/2110.05972v3
• Date: Thu, 20 Oct 2022 16:03:08 GMT
• Title: Dynamics of Spin Helices in the One-Dimensional $XX$ Model
• Authors: Darren Pereira and Erich J. Mueller
• Abstract summary: We analytically study the dynamics of spin helices in the one-dimensional $XX$ model. We find a separation of timescales between the in-plane and out-of-plane spin dynamics. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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