Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 334, Issue 1, Pages 433-471Publisher
SPRINGER
DOI: 10.1007/s00220-014-2167-x
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Funding
- Institute for Quantum Information and Matter, an NSF Physics Frontiers Center
- Gordon and Betty Moore Foundation [GBMF1250]
- AFOSR [FA8750-12-2-0308]
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We consider interacting, charged spins on a torus described by a gapped Hamiltonian with a unique groundstate and conserved local charge. Using quasi-adiabatic evolution of the groundstate around a flux-torus, we prove, without any averaging assumption, that the Hall conductance of the groundstate is quantized in integer multiples of e (2)/h, up to exponentially small corrections in the linear size L. In addition, we discuss extensions to the fractional quantization case under an additional topological order assumption on the degenerate groundstate subspace.
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