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. doi:10.1063/5.0022944. 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.
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| 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. | |||||||||
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| Issue or Number: | 10 | |||||||||
| DOI: | 10.1063/5.0022944 | |||||||||
| 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: | 16 Nov 2021 18:46 |
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