Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain
Abstract
Using the framework of nonlinear fluctuating hydrodynamics (NFH), we examine equilibrium spatiotemporal correlations in classical ferromagnetic spin chains with nearest neighbor interactions. In particular, we consider the classical XXZHeisenberg spin chain (also known as Lattice LandauLifshitz or LLL model) evolving deterministically and chaotically via Hamiltonian dynamics, for which energy and zmagnetization are the only locally conserved fields. For the easyplane case, this system has a lowtemperature regime in which the difference between neighboring spin's angular orientations in the XY plane is an almost conserved field. According to the predictions of NFH, the dynamic correlations in this regime exhibit a heat peak and propagating sound peaks, all with anomalous broadening. We present a detailed molecular dynamics test of these predictions and find a reasonably accurate verification. We find that, in a suitable intermediate temperature regime, the system shows two sound peaks with KardarParisiZhang (KPZ) scaling and a heat peak where the expected anomalous broadening is less clear. In high temperature regimes of both easy plane and easy axis case of LLL, our numerics show clear diffusive spin and energy peaks and absence of any sound modes, as one would expect. We also simulate an integrable version of the XXZmodel, for which the ballistic component instead moves with a broad range of speeds rather than being concentrated in narrower peaks around the sound speed.
 Publication:

Journal of Statistical Physics
 Pub Date:
 October 2019
 DOI:
 10.1007/s1095501902397y
 arXiv:
 arXiv:1901.00024
 Bibcode:
 2019JSP...180..238D
 Keywords:

 Hydrodynamics;
 Dynamical correlations;
 Heisenberg spin chain;
 Condensed Matter  Statistical Mechanics
 EPrint:
 32 pages, 16 figures