Anomalous Spin Diffusion in One-Dimensional Antiferromagnets

The problem of characterizing low-temperature spin dynamics in antiferromagnetic spin chains has so far remained elusive. Here we reinvestigate it by focusing on isotropic antiferromagnetic chains whose low-energy effective field theory is governed by the quantum nonlinear sigma model. Employing an exact nonperturbative theoretical approach, we analyze the low-temperature behavior in the vicinity of nonmagnetized states and obtain exact 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 semiclassical regime to a strongly interacting quantum regime characterized by zero spin Drude weight and diverging spin conductivity, indicating superdiffusive spin dynamics. The dynamical exponent of spin fluctuations is argued to belong to the Kardar-Parisi-Zhang universality class. Furthermore, by employing numerical time-dependent density matrix renormalization group simulations, we find robust evidence that the anomalous spin transport persists also at high temperatures, irrespective of the spectral gap and integrability of the model.