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arXiv · 1502.01232

Differential geometric invariants for time-reversal symmetric Bloch-bundles: the "Real" case

Giuseppe De Nittis·Kiyonori Gomi
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Abstract

Topological quantum systems subjected to an even (resp. odd) time-reversal symmetry can be classified by looking at the related "Real" (resp. "Quaternionic") Bloch-bundles. If from one side the topological classification of these time-reversal vector bundle theories has been completely described in [DG1] for the "Real" case and in [DG2] for the "Quaternionic" case, from the other side it seems that a classification in terms of differential geometric invariants is still missing in the literature. With this article (and its companion [DG3]) we want to cover this gap. More precisely, we extend in an equivariant way the theory of connections on principal bundles and vector bundles endowed with a time-reversal symmetry. In the "Real" case we generalize the Chern-Weil theory and we showed that the assignment of a "Real" connection, along with the related differential Chern class and its holonomy, suffices for the classification of "Real" vector bundles in low dimensions.

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Giuseppe De Nittis, Kiyonori Gomi. 2016-05-17. Differential geometric invariants for time-reversal symmetric Bloch-bundles: the "Real" case. https://doi.org/10.1063/1.4948742

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