Bulk-edge correspondence in topological pumping

The topological pumping proposed in 1980s and recently realized by cold atom experiments is revisited from the view point of the bulk-edge correspondence. For a system with boundaries, a different form of the pumped charge is derived by the Berry connection in the temporal gauge that corresponds to the shift of the center of mass (c.m.). Even with boundaries, the pumped charge is carried by the bulk and its quantization is guaranteed by the discontinuities of the c.m. associated with the edge states. This is a modified Laughlin argument based on the local U(1) invariance, although the physics behind it is quite different.