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arXiv:2103.07866 · Physical Review X

Transverse Spin Dynamics in the Anisotropic Heisenberg Model Realized with Ultracold Atoms

Niklas Jepsen, Wen Wei Ho, Jesse Amato-Grill, Ivana Dimitrova, Eugene Demler, Wolfgang Ketterle

Published Dec 17, 2021• 65 citations
arXivHTMLPDF

Abstract

In Heisenberg models with exchange anisotropy, transverse spin components are not conserved and can decay not only by transport, but also by dephasing.Here, we utilize ultracold atoms to simulate the dynamics of 1D Heisenberg spin chains and observe fast, local spin decay controlled by the anisotropy.However, even for isotropic interactions, we observe dephasing due to a new effect: an effective magnetic field created by superexchange.If spatially uniform, it leads only to uniform spin precession and is, therefore, typically ignored.However, we show through experimental studies and extensive numerical simulations how this superexchange-generated field is relevant and leads to additional dephasing mechanisms over the exchange anisotropy: There is dephasing due to (i) inhomogeneity of the effective field from variations of lattice depth between chains; (ii) a twofold reduction of the field at the edges of finite chains; and (iii) fluctuations of the effective field due to the presence of mobile holes in the system.The latter is a new coupling mechanism between holes and magnons.All these dephasing mechanisms have not been observed before with ultracold atoms and illustrate basic properties of the underlying Hubbard model.

DOI
10.1103/physrevx.11.041054

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In Heisenberg models with exchange anisotropy, transverse spin components are not conserved and can decay not only by transport, but also by dephasing.Here, we utilize ultracold atoms to simulate the dynamics of 1D Heisenberg spin chains and observe fast, local spin decay controlled by the anisotropy.However, even for isotropic interactions, we observe dephasing due to a new effect: an effective magnetic field created by superexchange.If spatially uniform, it leads only to uniform spin precession and is, therefore, typically ignored.However, we show through experimental studies and extensive numerical simulations how this superexchange-generated field is relevant and leads to additional dephasing mechanisms over the exchange anisotropy: There is dephasing due to (i) inhomogeneity of the effective field from variations of lattice depth between chains; (ii) a twofold reduction of the field at the edges of finite chains; and (iii) fluctuations of the effective field due to the presence of mobile holes in the system.The latter is a new coupling mechanism between holes and magnons.All these dephasing mechanisms have not been observed before with ultracold atoms and illustrate basic properties of the underlying Hubbard model.
In this work, we study the transport properties of the anisotropic Heisenberg model in a disordered magnetic field and in the presence of dephasing due to external degrees of freedom. Without dephasing, the model can display, depending on parameter values, the whole range of possible transport regimes: ideal ballistic conduction, diffusive, or ideal insulating behavior. We show that the presence of dephasing induces normal diffusive transport in a wide range of parameters. We also analyze the dependence of spin conductivity on the dephasing strength. In addition, by analyzing the decay of the spin–spin correlation function, we find a long-range order for finite chain sizes. All our results for a one-dimensional spin chain at infinite temperature can be equivalently rephrased for strongly interacting disordered spinless fermions.
We study spin transport in the one-dimensional anisotropic S=1S=1S=1 Heisenberg model. Particular emphasis is given to dynamics at infinite temperature, where current autocorrelations and spatiotemporal correlation functions are obtained by means of an efficient pure-state approach based on the concept of typicality. Our comprehensive numerical analysis unveils that high-temperature spin transport is diffusive in the easy-axis regime for strong exchange anisotropies. This finding is based on the combination of numerous signatures, such as (i) Gaussian spreading of correlations, (ii) a time-independent diffusion coefficient, (iii) power-law decay of equal-site correlations, (iv) exponentially decaying long-wavelength modes, and (v) Lorentzian line shapes of the dynamical structure factor. Moreover, we provide evidence that some of these signatures are not exclusively restricted to the infinite-temperature limit but can persist at lower temperatures as well, where we complement our results by additional quantum Monte Carlo simulations of large systems. In contrast to the easy-axis regime, we show that in the case of an isotropic chain, the signatures (i)--(v) are much less pronounced or even entirely absent, suggesting the existence of anomalous spin transport despite the nonintegrability of the model. Eventually, upon introducing a random on-site magnetic field, we observe a breakdown of diffusion and distinctly slower dynamics. In particular, our results exhibit qualitative similarities to disordered spin-1/21/21/2 chains and might be consistent with the onset of many-body localization in the S=1S=1S=1 model for sufficiently strong disorder.
A spinless Bose-Hubbard model in a one-dimensional (1D) double-chain tilted lattice is numerically studied at unit filling per cell. When each atom is localized in a two-site cell, the low-energy effective model gives rise to an exact textbook model of the 1D transverse Ising model via superexchange interaction. To validate the effective transverse Ising model, we calculate the energy spectrum and the nearest-neighbor correlation functions of the states in a subspace of the Bose-Hubbard model which is equivalent to the Hilbert space of a spin-1/2 magnetic model. The results show good consistency with the effective transverse Ising model, and we show that it is possible to simulate the dynamical quantum phase transition of the 1D transverse Ising model exactly with such a double-chain Bose-Hubbard model. Our results may provide some inspirations for realizing and exploring an exact 1D transverse Ising model in ultracold neutral atom systems.
We report the observation of electron spin interactions between Rydberg atoms, which are driven by spin-orbit coupling through second-order dipole perturbation and exhibit a spatial anisotropy governed by the atomic configuration. Specifically, we observe coherent electron spin exchange dynamics, with the measured coupling strength agreeing well with both numerical calculations and theoretical models. Furthermore, we show that global microwave dressing enables active engineering and dynamical freezing of the spin exchange by introducing a differential AC Stark shift between the participating states. Additionally, we achieve tunability of the interaction by applying a stronger magnetic field, which effectively modifies the energy contributions of the underlying spin-orbit coupling channels. Finally, measuring spin dynamics in one-dimensional multi-atom chains aligned parallel or perpendicular to the magnetic field provides a self-consistent validation of the anisotropic XXZ framework. This electron spin interaction natively features spin-position coupling and enables a natural mapping onto the Heisenberg-Kitaev model. Our findings reveal a new class of electron spin-spin interactions among Rydberg atoms, expanding the scope of quantum simulation with Rydberg atom arrays.
Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups, it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties that are usually relevant in solid-state many-body systems. In this paper, we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result, we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states, we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. The comparison reveals which aspects of non-equilibrium dynamics can, as in equilibrium, be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian.
By exploiting density-matrix renormalization group techniques, we investigate the spin dynamics of a spin-1/2 one-dimensional J 1 - J 2 XXZ model with competing ferromagnetic J 1 and antiferromagnetic J 2 exchange couplings under applied magnetic fields. Numerical results of spin excitation spectra show that in the field-induced spin quadrupole regime, the longitudinal component has a gapless mode and the transverse component has a gapped mode irrespective of the exchange anisotropy. The excitation gap of the transverse spin excitation increases as the exchange anisotropy increases over the XY-like and Ising-like regions, demonstrating that two-magnon bound states are stabilized due to the easy-axis anisotropy.