Hydrodynamic theory of spinon spin current.

Fractionalized quasi-particles of the Heisenberg spin-1/2 chain have been extensively probed by inelastic neutron scattering, electron spin, and nuclear magnetic resonances and other dynamical probes in the past. Here we present a theoretical analysis of the spinon spin current between the Heisenberg spin-1/2 chain and nonmagnetic conductor in the presence of the external magnetic field. We find that the residual backscattering interaction between spinons controls the low-temperature spinon current. Specifically, the current vanishes when the spin chain is tuned, by varying exchange interaction between the next-nearest spins, to the non-interacting spinon point. Our approximate analytical calculations are well supported by numerical results based on matrix-product-state techniques.