Classification of "Quaternionic" Bloch-Bundles Topological Quantum Systems of Type AII
de Nittis G, Gomi K (2015)
Publication Status: Published
Publication Type: Journal article
Publication year: 2015
Journal
Publisher: Springer Verlag (Germany)
Book Volume: 339
Pages Range: 1-55
Journal Issue: 1
DOI: 10.1007/s00220-015-2390-0
Abstract
We provide a classification of type AII topological quantum systems in dimension d = 1, 2, 3, 4. Our analysis is based on the construction of a topological invariant, the FKMM-invariant, which completely classifies "Quaternionic" vector bundles (a.k.a. "symplectic" vector bundles) in dimension . This invariant takes value in a proper equivariant cohomology theory and, in the case of examples of physical interest, it reproduces the familiar Fu-Kane-Mele index. In the case d = 4 the classification requires a combined use of the FKMM-invariant and the second Chern class. Among the other things, we prove that the FKMM-invariant is a bona fide characteristic class for the category of "Quaternionic" vector bundles in the sense that it can be realized as the pullback of a universal topological invariant.
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APA:
de Nittis, G., & Gomi, K. (2015). Classification of "Quaternionic" Bloch-Bundles Topological Quantum Systems of Type AII. Communications in Mathematical Physics, 339(1), 1-55. https://doi.org/10.1007/s00220-015-2390-0
MLA:
de Nittis, Giuseppe, and Kiyonori Gomi. "Classification of "Quaternionic" Bloch-Bundles Topological Quantum Systems of Type AII." Communications in Mathematical Physics 339.1 (2015): 1-55.
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