Quantization of Hall Conductance for Interacting Electrons on a Torus
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.
Additional Information© 2014 Springer-Verlag Berlin Heidelberg. Received: 28 October 2013; Accepted: 20 June 2014. MBH thanks M. Freedman, C. Nayak, and T. Osborne for useful discussions. SMt hanks B. Nachtergaele for useful discussions on Lieb–Robinson bounds. SM acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant #GBMF1250 and by the AFOSR Grant #FA8750-12-2-0308.
Submitted - 1306.1258v2.pdf