Subdiffusive hydrodynamics of nearly integrable anisotropic spin chains

Significance

While charge transport is known to be anomalous at low temperature in low-dimensional interacting systems, strong anomalies can be present at high temperature as well. Using the paradigmatic example of the quantum XXZ spin chain, we show that the presence of spin dephasing or generic additional Hamiltonian interactions leads to a broad regime of subdiffusive spin transport due to the interplay of emergent dynamical constraints and the effective screening of the relevant quasiparticle excitations. Although ordinary diffusion is eventually recovered at long times, the diffusion constant is shown to be nonperturbative and a discontinuous function of the strength of the external couplings.

Abstract

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.