Spin hydrodynamics in the S=1/2 anisotropic Heisenberg chain

We study the finite-temperature dynamical spin susceptibility of the one-dimensional (generalized) anisotropic Heisenberg model within the hydrodynamic regime of small wave vectors and frequencies. Numerical results are analyzed using the memory-function formalism with the central quantity being the spin-current decay rate gamma (q, omega). It is shown that in a generic nonintegrable model the decay rate is finite in the hydrodynamic limit, consistent with normal spin-diffusion modes. On the other hand, in the gapless integrable model within the XY regime of anisotropy Delta < 1 the behavior is anomalous with vanishing gamma (q, omega = 0) alpha |q|, in agreement with dissipationless uniform transport. Furthermore, in the integrable system the finite-temperature q = 0 dynamical conductivity sigma(q = 0, omega) reveals besides the dissipationless component a regular part with vanishing sigma(reg)(q = 0, omega -> 0) -> 0.