Quantization of Hall Conductance for Interacting Electrons on a Torus
Abstract
We consider interacting, charged spins on a torus described by a gapped Hamiltonian with a unique groundstate and conserved local charge. Using quasiadiabatic evolution of the groundstate around a fluxtorus, 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 February 2015
 DOI:
 10.1007/s002200142167x
 arXiv:
 arXiv:1306.1258
 Bibcode:
 2015CMaPh.334..433H
 Keywords:

 Quantum Physics;
 Mathematical Physics;
 81V70;
 82B10;
 82B20
 EPrint:
 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