Rational indices for quantum ground state sectors
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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 that preserves the ground state space, we associate an index that is an integer multiple of 1/𝑝, where 𝑝 is the ground state degeneracy. We prove that the index is additive under composition of unitaries. This formalism gives rise to several applications: fractional quantum Hall conductance, a fractional Lieb–Schultz–Mattis (LSM) theorem that generalizes the standard LSM to systems where the translation-invariance is broken, and the interacting generalization of the Avron–Dana–Zak relation between the Hall conductance and the filling factor.
Original language | English |
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Article number | 011901 |
Journal | Journal of Mathematical Physics |
Volume | 62 |
Issue number | 1 |
Number of pages | 21 |
ISSN | 0022-2488 |
DOIs | |
Publication status | Published - 2021 |
ID: 291599561