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arXiv:2404.17558 · Physical Review A

Dynamics of spin helices in the diluted one-dimensional X X model

Darren Pereira, Erich J. Mueller

Published Aug 13, 2024• 2 citations
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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 $x\text{\ensuremath{-}}z$ spin helices in the one-dimensional $XX$ model. We calculate the exact spin dynamics by mapping onto a system of noninteracting 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.

DOI
10.1103/physreva.110.023313

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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\ensuremath-zx\text{\ensuremath{-}}zx\ensuremath-z spin helices in the one-dimensional XXXXXX model. We calculate the exact spin dynamics by mapping onto a system of noninteracting 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 XXZXXZXXZ model with arbitrary anisotropies, we validate a matrix-product-state technique which might be used to model the experiments in those settings.
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\mathit{XX}XX model. We use a Jordan-Wigner transformation to map the spin chain onto a noninteracting 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 ${t}^{\ensuremath{-}1/2}$ at long time, in contrast to the experimentally observed exponential decay.
Motivated by cold atom experiments, we analytically study the dynamics of spin helices in the 1D XX model. Using the Jordan-Wigner transformation to map spins into fermions, we calculate the evolution of the spin helix over time. The fermions are non-interacting, with simple equations of motion. Nonetheless, the calculation is non-trivial, as the spin-helix initial condition corresponds to a highly non-equilibrium distribution of the fermions. We compare the resulting dynamics to a semiclassical model, and find qualitatively similar out-of-plane dynamics. The in-plane dynamics, however, are dramatically different. The spins decohere over time, resulting in a t−1/2t^{-1/2}t−1/2 decay of the spin-spin correlation function, which can be contrasted to exponential decay seen in recent experiments.
Motivated by recent cold-atom experiments, we study the relaxation of spin helices in quantum XXZ spin chains. The experimentally observed relaxation of spin helices follows scaling laws that are qualitatively different from linear-response transport. We construct a theory of the relaxation of such spin helices, combining generalized hydrodynamics with diffusive corrections and a generalized form of the local density approximation. Although helices are far from local equilibrium, our hydrodynamic approach reproduces the experimentally observed relaxational dynamics and also predicts the late-time relaxation, which is outside the experimentally accessible timescales. In particular, our theory explains the existence of temporal regimes with apparent anomalous diffusion, as well as the asymmetry between positive and negative anisotropy regimes at short and intermediate times.
We use the density matrix renormalization group method to study the properties of the one-dimensional Kondo-Heisenberg model doped with Kondo holes. We find that the perturbation of the Kondo holes to the local hybridization exhibits spatial oscillation pattern and its amplitude decays exponentially with distance away from the Kondo hole sites. The hybridization oscillation is correlated with both the charge density oscillation of the conduction electrons and the oscillation in the correlation function of the Heisenberg spins. In particular, we find that the oscillation wavelength for intermediate Kondo couplings is given by the Fermi wavevector of the large Fermi surface even before it is formed. This suggests that heavy electrons responsible for the oscillation are already present in this regime and start to accumulate around the to-be-formed large Fermi surface in the Brillouin zone.
We study interaction quenches of the Fermi-Hubbard model initiated from various high-temperature and high-energy states, motivated by cold atom experiments, which currently operate above the ordering temperature(s). We analytically calculate the dynamics for quenches from these initial states, which are often strongly interacting, to the noninteracting limit. Even for high-temperature uncorrelated initial states, transient connected correlations develop. These correlations share many features for all considered initial states. We observe light-cone spreading of intertwined spin and density correlations. The character of these correlations is quite different from their low-temperature equilibrium counterparts: for example, the spin correlations can be ferromagnetic. We also show that an initially localized hole defect affects spin correlations near the hole, suppressing their magnitude and changing their sign.
In this Letter, we investigate spin dynamics of a two-component Bose gas with spin-orbit coupling realized in cold atom experiments. We derive coupled hydrodynamic equations for number and spin densities as well as their associated currents. Specializing to the quasi-one-dimensional situation, we obtain analytic solutions of the spin helix structure and its dynamics in both adiabatic and diabatic regimes. In the adiabatic regime, the transverse spin decays parabolically in the short-time limit and exponentially in the long-time limit, depending on initial polarization. In contrast, in the diabatic regime, transverse spin density and current oscillate in a way similar to the charge-current oscillation in an undamped LC circuit. The effects of Rabi coupling on the short-time spin dynamics is also discussed. Finally, using realistic experimental parameters for ^{87}Rb, we show that the timescales for spin dynamics is of the order of milliseconds to a few seconds and can be observed experimentally.