  Sequential plateaux transitions of quantum spin chains ($S$=1,3/2,2 and 3)
are demonstrated by a spin pump using dimerization and staggered magnetic field
as synthetic dimensions. The bulk is characterized by the Chern number
associated with the boundary twist and the pump protocol as a time. It counts
the number of critical points in the loop that is specified by the $Z_2$ Berry
phases. With open boundary condition, discontinuity of the spin weighted center
of mass due to emergent effective edge spins also characterizes the pump as the
bulk-edge correspondence. It requires extra level crossings in the pump as a
super-selection rule that is consistent with the Valence Bond Solid (VBS)
picture.
