Quantum spin pump on a finite antiferromagnetic chain through bulk states

We studied the possibility of the spin pump in a S=1/2 antiferromagnetic chain. The spin chain is mapped into a fermion system and bosonization is utilized to transform the equation of motion to a sine-Gordon equation. The sine-Gordon equation on a finite chain with different boundary conditions is solved. Among numerous solutions, the static soliton is compatible with the original physical system. By varying adiabatically a angle in the phase space composed of applied electric and magnetic fields, the spin states change between the Neel state and dimer state and a quantized spin is transported by the bulk state from one end of the system to the other.