Index Pairings in Presence of Symmetries with Applications to Topological Insulators

Großmann J, Schulz-Baldes H (2016)

Publication Type: Journal article, Original article

Publication year: 2016

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 343

Pages Range: 477-513

Journal Issue: 2

URI: http://link.springer.com/article/10.1007/s00220-015-2530-6

DOI: 10.1007/s00220-015-2530-6

Abstract

In a basic framework of a complex Hilbert space equipped with a complex conjugation and an involution, linear operators can be real, quaternionic, symmetric or anti-symmetric, and orthogonal projections can furthermore be Lagrangian. This paper investigates index pairings of projections and unitaries submitted to such symmetries. Various scenarios emerge: Noether indices can take either arbitrary integer values or only even integer values or they can vanish and then possibly have secondary $Z_{2}$ -invariants. These general results are applied to prove index theorems for the strong invariants of disordered topological insulators. The symmetries come from the Fermi projection (K-theoretic part of the pairing) and the Dirac operator (K-homological part of the pairing depending on the dimension of physical space).

Authors with CRIS profile

Julian Großmann Professur für Mathematik (Mathematische Physik) Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

How to cite

APA:

Großmann, J., & Schulz-Baldes, H. (2016). Index Pairings in Presence of Symmetries with Applications to Topological Insulators. Communications in Mathematical Physics, 343(2), 477-513. https://dx.doi.org/10.1007/s00220-015-2530-6

MLA:

Großmann, Julian, and Hermann Schulz-Baldes. "Index Pairings in Presence of Symmetries with Applications to Topological Insulators." Communications in Mathematical Physics 343.2 (2016): 477-513.

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