We study finite-temperature magnetization transport in a one-dimensional anisotropic Heisenberg model, focusing in particular on the gapped phase. Using numerical simulations by two different methods, a propagation of localized wave packets and a study of nonequilibrium steady states of a master equation in a linear-response regime, we conclude that the transport at finite temperatures is diffusive. With decreasing temperature the diffusion constant increases, possibly exponentially fast. This means that at low temperatures the transition from ballistic to asymptotic diffusive behavior happens at very long times. We also study dynamics of initial domain-wall-like states, showing that on the attainable time scales they remain localized.
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.
It is well established that at zero magnetic field
h=0, the spin diffusion constant of the spin-
21 XXZ chain is for anisotropy $\mathrm{\ensuremath{\Delta}}>1$ finite for both low and high temperatures, implying that the type of spin transport is normal diffusive. Although it is expected that this holds for all finite temperatures
T>0, the calculation of the spin diffusion constant for all
T is typically intractable. Here we consider a class of energy eigenstates that exist both for anisotropies $\mathrm{\ensuremath{\Delta}}=1$ and $\mathrm{\ensuremath{\Delta}}>1$. We show that at the isotropic point their contributions are behind the diffusion constant being infinite, spin transport being anomalous superdiffusive for
T>0. That for $\mathrm{\ensuremath{\Delta}}>1$ such states do not contribute to the diffusion constant is shown to imply it is finite, spin transport being normal diffusive for
T>0. By combining the connection through a Jordan-Wigner transformation of the spin-
21 XXZ chain to the one-dimensional (1D) lattice spinless fermion model at zero chemical potential $\ensuremath{\mu}=0$, for $V/J\ensuremath{\ge}1$ with its Bethe-ansatz solution, where
V is the nearest-neighbor Coulomb repulsion and
J=2t is twice the hopping integral
t, in this paper we also address the issue of the
T>0 charge transport of that model at $\ensuremath{\mu}=0$. It is found to be anomalous superdiffusive for
V/J=1 and normal diffusive for
V/J>1. Our results thus open the door to a key advance in the understanding for all finite temperatures
T>0 of the spin transport in the spin-
21 XXZ chain at
h=0 for anisotropy $\mathrm{\ensuremath{\Delta}}\ensuremath{\ge}1$ and of the charge transport in the 1D lattice spinless fermion model at $\ensuremath{\mu}=0$ for $V/J\ensuremath{\ge}1$.
Spin transport in the anisotropic Heisenberg chain is typically investigated theoretically with respect to the finiteness of transport coefficients only. Assuming their finiteness at high temperatures, we develop a concrete quantitative picture of the diffusion constant/(dc-)conductivity as a function of both the anisotropy parameter Δ and the spin quantum number s, going beyond the most commonly considered case s=1/2. Using this picture, we enable the comparison of finite transport coefficients from complementary theoretical methods on a quantitative level, having more significance than the finiteness alone. Our method is essentially based on an application of the time-convolutionless projection operator technique to current autocorrelations. This technique, although being a perturbation theory in Δ, is found to be applicable, even if Δ is not small. This finding supports the applicability to a wider class of strongly interacting many-particle quantum systems.
The problem of spin diffusion is studied numerically in the one-dimensional classical Heisenberg model using a deterministic odd-even spin precession dynamics. We demonstrate that spin diffusion in this model is normal in the infinite-temperature limit and one obtains a long-time diffusive tail in the decay of the autocorrelation function. Some variations of the model with different coupling schemes and anisotropy are also studied and we find normal diffusion in all of them. A systematic finite-size analysis also suggests normal diffusive spreading of spin fluctuations, contrary to previous claims of anomalous diffusion. We also briefly discuss spin diffusion in this model at finite temperatures.
We study spin transport in the one-dimensional anisotropic
S=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-
1/2 chains and might be consistent with the onset of many-body localization in the
S=1 model for sufficiently strong disorder.