Rational indices for quantum ground state sectors

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  • Sven Bachmann
  • Alexander Fransiscus J Bols
  • Wojciech De Roeck
  • Martin Fraas
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.
TidsskriftJournal of Mathematical Physics
Udgave nummer1
Antal sider21
StatusUdgivet - 2021

ID: 291599561