Diffusive spin transport of the spin-1/2 XXZ chain in the Ising regime at zero magnetic field and finite temperature

Abstract: The studies of this paper on the spin-1/2 XXZ chain at finite temperatures T>0 have two complementary goals. The first is to identify the spin carriers of all its Sq>0 energy eigenstates and to show that their spin elementary currents fully control the spin-transport quantities. Here Sq is the q-spin of the continuous SUq(2) symmetry of the model for anisotropy >1. To achieve this goal, our studies rely on a suitable exact physical-spin representation.Both the spin stiffness and the zero-field spin-diffusion constant are expressed in terms of thermal expectation values of the square of the elementary currents carried by the spin carriers. Our second goal is to confirm that the zero-field and finite-temperature spin transport is normal diffusive for anisotropy >1. We use two complementary methods that rely on an inequality for the T>0 spin stiffness and the above thermal expectation values, respectively, to show that the contributions to ballistic spin transport vanish. Complementarily, for T>0 and anisotropy >1, the spin-diffusion constant is found to be finite and enhanced upon lowering T, reaching its largest yet finite values at low temperatures. Evidence suggests that it diverges in the anisotropy limit to 1 for T>0, consistent with T>0 anomalous superdiffusive spin transport at anisotropy 1 and zero field.