Subdiffusive hydrodynamics of nearly integrable anisotropic spin chains

We address spin transport in the easy-axis Heisenberg spin chain subject to different integrability-breaking perturbations. We find subdiffusive spin transport characterized by dynamical exponent z = 4 up to a timescale parametrically long in the anisotropy. In the limit of infinite anisotropy, transport is subdiffusive at all times; for finite anisotropy, one eventually recovers diffusion at late times but with a diffusion constant independent of the strength of the perturbation and solely fixed by the value of the anisotropy. We provide numerical evidence for these findings, and we show how they can be understood in terms of the dynamical screening of the relevant quasiparticle excitations and effective dynamical constraints. Our results show that the diffusion constant of near-integrable diffusive spin chains is generically not perturbative in the integrability-breaking strength.

Automated summary

In this study, we investigate spin transport in the easy-axis Heisenberg spin chain subject to various integrability-breaking perturbations. We find that the spin transport exhibits subdiffusive behavior characterized by a dynamical exponent z = 4, which persists for a significantly long timescale in the presence of anisotropy. In the limit of infinite anisotropy, the transport remains subdiffusive at all times, while for finite anisotropy, diffusion eventually emerges at late times with a diffusion constant determined solely by the anisotropy value.