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Hall conductance and the statistics of flux insertions in gapped interacting lattice systems

Kapustin, Anton and Sopenko, Nikita (2020) Hall conductance and the statistics of flux insertions in gapped interacting lattice systems. Journal of Mathematical Physics, 61 (10). Art. No. 101901. ISSN 0022-2488. https://resolver.caltech.edu/CaltechAUTHORS:20201002-092331999

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Abstract

We study charge transport for zero-temperature infinite-volume gapped lattice systems in two dimensions with short-range interactions. We show that the Hall conductance is locally computable and is the same for all systems that are in the same gapped phase. We provide a rigorous version of Laughlin’s flux-insertion argument, which shows that for short-range entangled systems, the Hall conductance is an integer multiple of e²/h. We show that the Hall conductance determines the statistics of flux insertions. For bosonic short-range entangled systems, this implies that the Hall conductance is an even multiple of e²/h. Finally, we adapt a proof of quantization of the Thouless charge pump to the case of infinite-volume gapped lattice systems in one dimension.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1063/5.0022944DOIArticle
https://arxiv.org/abs/2006.14151arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Sopenko, Nikita0000-0002-8479-1924
Additional Information:© 2020 Published under license by AIP Publishing. Submitted: 24 July 2020; Accepted: 30 August 2020; Published Online: 1 October 2020. This research was supported, in part, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. A.K. was also supported by the Simons Investigator Award. N.S. gratefully acknowledges the support of the Dominic Orr Fellowship at Caltech. Data Availability: Data sharing is not applicable to this article as no new data were created or analyzed in this study.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Dominic Orr Graduate FellowshipUNSPECIFIED
Issue or Number:10
Record Number:CaltechAUTHORS:20201002-092331999
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201002-092331999
Official Citation:Hall conductance and the statistics of flux insertions in gapped interacting lattice systems. Anton Kapustin, Nikita Sopenko. Journal of Mathematical Physics 61:10; doi: 10.1063/5.0022944
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105750
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 Oct 2020 16:33
Last Modified:02 Oct 2020 16:33

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