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Quantum Hall effect and the relative index for projections

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.

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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.

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Simon, Barry0000-0003-2561-8539
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.
Funding AgencyGrant Number
Binational Science Foundation (USA-Israel)80-00365
Akademie der Wissenschaften zu BerlinUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)UNSPECIFIED
Issue or Number:17
Classification Code:PACS numbers: 72.20.My, 02.40.+m
Record Number:CaltechAUTHORS:20180313-142926573
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85284
Deposited By: Tony Diaz
Deposited On:13 Mar 2018 21:39
Last Modified:15 Nov 2021 20:27

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