TY - JOUR

T1 - Rational indices for quantum ground state sectors

AU - Bachmann, Sven

AU - Bols, Alexander Fransiscus J

AU - De Roeck, Wojciech

AU - Fraas, Martin

PY - 2021

Y1 - 2021

N2 - 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/푝, where 푝 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.

AB - 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/푝, where 푝 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.

U2 - 10.1063/5.0021511

DO - 10.1063/5.0021511

M3 - Journal article

VL - 62

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 1

M1 - 011901

ER -