Rational indices for quantum ground state sectors

We consider charge transport for interacting many-body systems with a gapped ground state subspace that is finitely degenerate and topologically ordered. To any locality-preserving, charge-conserving unitary preserves the space, we associate an index integer multiple of 1/p, where p degeneracy. prove additive under composition unitaries. This formalism gives rise to several applications: fractional quantum Hall conductance, Lieb–Schultz–Mattis (LSM) theorem generalizes standard LSM translation-invariance broken, generalization Avron–Dana–Zak relation between conductance filling factor.