Quantum Pump for Spin and Charge Transport in a Luttinger Liquid

We study two different parametric pumps -- one for pumping spin currents, the other for charge currents -- in interacting quantum wires. We find that, as a function of pumping frequency, the spin or charge pumped per cycle has a nonuniversal crossover -- depending on pumping details -- between two universal fixed point values of 0 and twice the electronic spin or charge quantum number. The direction of flow between these two fixed points depends on whether the interactions are repulsive or attractive, while the quantization itself is a signature of interactions