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

TL;DR

This paper investigates the spin transport properties of the anisotropic Heisenberg chain at finite temperature, revealing normal diffusion in nonintegrable cases and anomalous dissipationless behavior in integrable regimes, using numerical and analytical methods.

Contribution

It provides a detailed analysis of spin dynamics in the anisotropic Heisenberg model, highlighting differences between integrable and nonintegrable cases with new insights into spin diffusion and dissipation.

Findings

Finite spin-current decay rate in nonintegrable models indicates normal diffusion.

In the XY regime of the integrable model, decay rate vanishes proportionally to |q|, indicating anomalous transport.

Dynamical conductivity shows dissipationless and regular parts, with the regular part vanishing at low frequencies.

Abstract

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) proportional to |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 to 0) to 0.