Published October 22, 1990
| Published
Journal Article
Open
Quantum Hall effect and the relative index for projections
- Creators
- Avron, Joseph E.
- Seiler, Ruedi
-
Simon, Barry
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.
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.Attached Files
Published - PhysRevLett.65.2185.pdf
Files
PhysRevLett.65.2185.pdf
Files
(180.6 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:014f464d498e6be9dc657b17916b449c
|
180.6 kB | Preview Download |
Additional details
- Eprint ID
- 85284
- Resolver ID
- CaltechAUTHORS:20180313-142926573
- 80-00365
- Binational Science Foundation (USA-Israel)
- Technion
- DMS-8807816
- NSF
- Akademie der Wissenschaften zu Berlin
- Deutsche Forschungsgemeinschaft (DFG)
- Created
-
2018-03-13Created from EPrint's datestamp field
- Updated
-
2021-11-15Created from EPrint's last_modified field