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Quantization of Hall Conductance for Interacting Electrons on a Torus

Hastings, Matthew B. and Michalakis, Spyridon (2015) Quantization of Hall Conductance for Interacting Electrons on a Torus. Communications in Mathematical Physics, 334 (1). pp. 433-471. ISSN 0010-3616. https://resolver.caltech.edu/CaltechAUTHORS:20150306-090338269

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s00220-014-2167-x DOIArticle
http://link.springer.com/article/10.1007%2Fs00220-014-2167-xPublisherArticle
http://arxiv.org/abs/1306.1258arXivDiscussion Paper
http://rdcu.be/ttdYPublisherFree ReadCube access
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.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationGBMF1250
Air Force Office of Scientific Research (AFOSR)FA8750-12-2-0308
Issue or Number:1
Record Number:CaltechAUTHORS:20150306-090338269
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150306-090338269
Official Citation:Hastings, M.B. & Michalakis, S. Commun. Math. Phys. (2015) 334: 433. doi:10.1007/s00220-014-2167-x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55577
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Mar 2015 18:25
Last Modified:03 Oct 2019 08:06

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