Anomalous spin diffusion in one-dimensional antiferromagnets

Understand

The problem of characterizing low-temperature spin dynamics in antiferromagnetic spin chains has so far remained elusive.

• We reinvestigate it by focusing on isotropic antiferromagnetic chains whose low-energy effective field theory is governed by the quantum non-linear sigma model.
• We outline an exact non-perturbative theoretical approach to analyse the low-temperature behaviour in the vicinity of non-magnetized states, and obtain explicit expressions for the spin diffusion constant and the NMR relaxation rate, which we compare with previous theoretical results in the literature.
• Surprisingly, in SU(2)-invariant spin chains in the vicinity of half-filling we find a crossover from the semi-classical regime to a strongly interacting quantum regime characterized by zero spin Drude weight and diverging spin conductivity, indicating super-diffusive spin dynamics.