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.
Communications in Mathematical Physics
- Pub Date:
- February 2015
- Quantum Physics;
- Mathematical Physics;
- 28 pages, 4 figures, This paper significantly simplifies the proof and tightens the bounds previously shown in arXiv:0911.4706 by the same authors. Updated to reflect published version