Topological classification of interaction-driven spin pumps

When adiabatically varied in time, certain one-dimensional band insulators allow for the quantized noiseless pumping of spin even in the presence of strong spin-orbit scattering. These spin pumps are closely related to the quantum spin Hall system, and their properties are protected by a time-reversal restriction on the pumping cycle. In this paper we study pumps formed of one-dimensional insulators with a time-reversal restriction on the pumping cycle and a bulk energy gap which arises due to interactions. We find that the correlated gapped phase can lead to novel pumping properties. In particular, systems with d different ground states can give rise to $d+1$ different classes of spin pumps, including a trivial class which does not pump quantized spin and d nontrivial classes allowing for the pumping of quantized spin /n on average per cycle, where 1≤n≤d. We discuss an example of a spin pump that transfers an average of spin /2 without transferring charge.