Shift and spin vector: New topological quantum numbers for the Hall fluids

We discuss some new quantum numbers (spin vector) for the Hall fluid, representing orbital spin degrees of freedom. We show that the spin vectors are quantized. In the absence of impurites, two Hall fluids with different spin vectors cannot change into each other without a phase transition and closing of the energy gap. In principle the spin vector can be measured through its coupling to the curvature of space. Our formalism may be described picturesquely as a unification of electromagnetism and ‘‘gravity’’ in condensed-matter physics.