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Topological Invariants in Fermi Systems with Time-Reversal Invariance

Avron, J. E. and Sadun, L. and Segert, J. and Simon, B. (1988) Topological Invariants in Fermi Systems with Time-Reversal Invariance. Physical Review Letters, 61 (12). pp. 1329-1332. ISSN 0031-9007. doi:10.1103/PhysRevLett.61.1329.

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We discuss topological invariants for Fermi systems that have time-reversal invariance. The TKN^2 integers (first Chern numbers) are replaced by second Chern numbers, and Berry's phase becomes a unit quaternion, or equivalently an element of SU(2). The canonical example playing much the same role as spin ½ in a magnetic field is spin ½ in a quadrupole electric field. In particular, the associated bundles are nontrivial and have ± 1 second Chern number. The connection that governs the adiabatic evolution coincides with the symmetric SU(2) Yang-Mills instanton.

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Simon, B.0000-0003-2561-8539
Additional Information:© 1988 American Physical Society. (Received 6 July 1988) We thank Peter Weichman for useful discussions. The research of one of us (J.E.A.) was partially supported by National Science Foundation Grants No. DMS-8416049 and No. BSF-84-00376. The research of another one of us (B.S.) was partially supported by National Science Foundation Grant No. DMS-8416049.
Funding AgencyGrant Number
Binational Science Foundation (USA-Israel)BSF-84-00376
Issue or Number:12
Classification Code:PACS numbers: 03.65.Bz, 02.40.+m
Record Number:CaltechAUTHORS:20180413-164425306
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85866
Deposited By: George Porter
Deposited On:16 Apr 2018 21:04
Last Modified:15 Nov 2021 20:32

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