Solitons and spin transport in an antiferromagnetic spin chain

We study the spin transport on a S=1/2 antiferromagnetic chain with external fields which provids a phase angle. The equation of motion becomes the sine-Gordon equation after Jordan-Wigner transformation and bosonization. Soliton solutions of the sine-Gordon equations for a system of finite length are found and the quantum fluctuations are calculated. The spin is transported as the soliton solutions evolves with the adiabatical variation of the phase angle in the phase space. We observe that the spin is transported by {\Delta}S=1, as the phase angle changes by the period of 2{\pi} when the quantum fluctuation enables the system makes transition between two solutions. This quantum spin transport is not affected by disturbance of environment.