Avron, Joseph E. and Seiler, Ruedi and Simon, Barry (1990) Quantum Hall effect and the relative index for projections. Physical Review Letters, 65 (17). pp. 2185-2188. ISSN 0031-9007. doi:10.1103/PhysRevLett.65.2185. https://resolver.caltech.edu/CaltechAUTHORS:20180313-142926573
![]() |
PDF
- Published Version
See Usage Policy. 180kB |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20180313-142926573
Abstract
We define the relative index, Index(P,Q), for a pair of infinite-dimensional projections on a Hilbert space to be the integer that is the natural generalization of dim(P)-dim(Q) in finite-dimensional vector spaces. We show that the Hall conductance for independent electrons in the plane is the relative index where P and Q project on the states below the Fermi energy for Hamiltonians that differ by a quantum flux and the Fermi energy is appropriately placed. This approach is closely related to, and sheds light on, Bellissard’s interpretation of the Hall conductance as an index.
Item Type: | Article | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Related URLs: |
| ||||||||||||
ORCID: |
| ||||||||||||
Additional Information: | © 1990 American Physical Society. Received 10 July 1990. This work is supported in part by the U.S.-Israel Binational Science Foundation under Grant No. 80-00365, by the Fund for the Promotion of Research at the Technion, and by U.S. NSF under Grant No. DMS-8807816. J.E.A. thanks Jean Bellissard and D. J. Thouless for useful conversations and B.S. thanks the Technion for its hospitality. R.S. acknowledges the support of the Akademie der Wissenschaften zu Berlin and the Deutsche Forschungsgemeinschaft. | ||||||||||||
Funders: |
| ||||||||||||
Issue or Number: | 17 | ||||||||||||
Classification Code: | PACS numbers: 72.20.My, 02.40.+m | ||||||||||||
DOI: | 10.1103/PhysRevLett.65.2185 | ||||||||||||
Record Number: | CaltechAUTHORS:20180313-142926573 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180313-142926573 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 85284 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Tony Diaz | ||||||||||||
Deposited On: | 13 Mar 2018 21:39 | ||||||||||||
Last Modified: | 15 Nov 2021 20:27 |
Repository Staff Only: item control page