Hydrodynamic relaxation of spin helices

Abstract

Motivated by recent cold atom experiments, we study the relaxation of spin helices in quantum XXZ spin chains. The experimentally observed relaxation of spin helices follows scaling laws that are qualitatively different from linear-response transport. We construct a theory of the relaxation of helices, combining generalized hydrodynamics (GHD) with diffusive corrections and the local density approximation. Although helices are far from local equilibrium (so GHD need not apply a priori), our theory reproduces the experimentally observed relaxational dynamics of helices. In particular, our theory explains the existence of temporal regimes with apparent anomalous diffusion, as well as the asymmetry between positive and negative anisotropy regimes.

Anomalous transport from hot quasiparticles in interacting spin chains

“…Spin helices are, in general, quite far from being locally thermal states, so the applicability of GHD to them can be questioned. However, one might expect that after some initial evolution, dephasing leads to local reduced density matrices that are well described by GGEs [149]. This intuition can be verified for free fermions, and was recently generalized to interacting systems using GHD in [149].…”